Answers
Answers:
[tex]\text{OA} = \cos(\alpha)\\\\\text{AB} = \sin(\alpha)\\\\\text{DC} = \tan(\alpha)\\\\[/tex]
You can use the word "alpha" without quotes in place of the symbol [tex]\alpha[/tex] if you want (though it will depend if your teacher allows it of course).
======================================================
Explanation:
Focus entirely on triangle AOB.
With respect to reference angle alpha (symbol [tex]\alpha[/tex]), the side OA is the adjacent side since it's the leg closest to or touching the reference angle.
In this same triangle, side OB is the hypotenuse. Because its the radius of the unit circle, we know that OB = 1.
We'll use the cosine rule to connect the adjacent over hypotenuse like so
[tex]\cos(\text{angle}) = \frac{\text{adjacent}}{\text{hypotenuse}}\\\\\cos(\alpha) = \frac{\text{OA}}{\text{OB}}\\\\\cos(\alpha) = \frac{\text{OA}}{1}\\\\\text{OA} = \cos(\alpha)\\\\[/tex]
So you'll type either [tex]\cos(\alpha)[/tex] or cos(alpha) into the box for OA.
----------------------------------------
We're still working with triangle AOB only.
Side AB is the opposite side with respect to reference angle alpha.
We can say
sin(angle) = opposite/hypotenuse
sin(alpha) = AB/OB
sin(alpha) = AB/1
AB = sin(alpha)
Basically it's almost identical to the previous section's steps, but we're using sine instead of cosine this time. Like before, you can type in either [tex]\sin(\alpha)[/tex] or sin(alpha) depending on your teacher's preferences.
----------------------------------------
This next section can be a bit tricky.
Sides AB and DC are parallel due to them being both vertical. We can use the AA (angle angle) similarity theorem to prove triangle BOA is similar to triangle DOC. The order of the letters is important. The order helps us see how the sides pair up, or how they correspond, so we can form the correct proportion.
The vertical sides of the triangles are AB and DC as mentioned earlier, so they form one fraction AB/DC. I'm dividing small over big.
Another fraction we can form is OA/OC which is dividing the horizontal legs (again small/big).
Overall, due to the similar triangles, we can set up this equation
AB/DC = OA/OC
We'll plug in what we found earlier. Also, OC = 1 because it's another radius of the same unit circle.
Lets solve for side DC.
AB/DC = OA/OC
sin(alpha)/DC= cos(alpha)/1
sin(alpha)*1 = DC*cos(alpha)
DC = sin(alpha)/cos(alpha)
DC = tan(alpha)
--------------------------------------
In summary, segments OA, AB and OC represent the cosine, sine and tangent of the reference angle alpha. These are visual ways to see how the trig ratios correspond to lengths of triangles when connecting them to the unit circle like this.
Side notes:
Point B is at the location (cos(alpha), sin(alpha)). Point D is at (1, tan(alpha)).Related Questions
(x+3)(x−1)
Cual seria su resultado
Answers
Answer:
x² -1x + 3x -3
= x² +2x -3
hope it helps
Write and graph an inequality to represent each situation.
The stock is worth at least $3.5
Answers
Answer:
Step-by-step explanation:
Let stock worth be x.
The inequality will be x ≥ 3.5
The graph will be a number line with numbers 1, 2, 3 , 4 , 5 , 6 . . .
Then darken a small circle at 3.5 and darken the line
moving towards 4, 5 , 6 . . . and finally end with an arrow mark. showing it goes to ∞
A newborn weighs 7 lb and 13 oz. How many grams (g) does he weigh?
Answers
Answer:
69
Step-by-step explanation:
si se vendieron 8 refrescos y cada uno tiene un costo de $9.50 ¿cuánto dinero colectó
con esa venta?
Answers
Is 0.01011011101111011111 rational or irrational?
Answers
Answer:
It is rational number.
Step-by-step explanation:
A rational number is any integer, fraction, terminating decimal, or repeating decimal.
Hope it is helpful....help
Sadie needs 3.1 yards to make one costume for each choir member in the play. How much fabric will she need if she has to make 5 costumes?
A.
15.5 yards
B.
10.5 yards
C.
18.6 yards
D.
16.5 yards
Answers
Answer:
A. 15.5 yards
Step-by-step explanation:
3.1 ×5=15.5
Heeeeeeeeeeelppppppppppppppppppp
Answers
A)
So please brainliest my answer I would really appreciate it and best of wishes!!
A ladder is put against a building. The building is 25 feet tall. The ladder's base is 13.5 feet from the building. Find the angle which the ladder makes with the ground.
Answers
the answer is 16.0 or 11.0
A table cost $ 495.00 There is a 9% tax. What is the final price?
Answers
Answer:
i also need help with these one please help
Step-by-step explanation:
Answer:
$539.55
Step-by-step explanation:
Can someone help me again with these math work?
Answers
Answer:
it look like its 4 and the 4 over 4/5 I think
You have decided after graduating from an institution beyond high school, you want to live on your own. You have entered a career with a net income of $4785 per month. You search the local area finding an amazing deal at Succex Apartment Homes in Grapevine, Texas. Floor plan C fits within your budget.
The apartment is empty when you move in, so you will have to decorate making some adjustments on your financial budget to afford a place to stay. A floor plan will be provided to you.
What is the area of the Masters Bedroom? *
16.51 square meters
19.11 square meters
14.04 square meters
29.4 square meters
Answers
Answer:
16.51 square meters.
Step-by-step explanation:
The area of the bedroom can be determine by the formula:
Area = Length * Width
Length of the room is 4.3 meters while width of the master bedroom is 2.4 meters. The length of the closet is 0.6 meters and width is 1.5 meters. The area can be determined by:
2.4 - 1.5 = 0.9 meters
4.3 - 0.6 = 3.7 meters
Area = 3.7 * 0.9
= 3.3 meters.
Conversion from meters to square meters = 3.3^2
Area = 16.51 square meters.
of the 10 people attending a seminar, 5 have gray hair.
What is the probability that a randomly selected person will have gray hair?
Answers
Answer:
1/2
Step-by-step explanation:
So we know that there is a total of 10 people.
5 of these have grey hair.
To find the chances of a somone having grey hair, we need to divide people with grey hair over total people:
[tex]\frac{value}{total} =probability[/tex]
This is the same division we use to find things such as percentage and ratio as well.
Now lets plug in our numbers and solve:
[tex]\frac{5}{10}=\frac{1}{2}[/tex]
So half of the people have grey hair.
Or(in percentage):
The probability is 50% that someone will have grey hair.
Hope this hepls!
real fourth roots of -625
Answers
Answer:
-5
Step-by-step explanation:
[tex]\sqrt[4]{-625}[/tex]
=[tex]\sqrt[4]{-5*-5*-5*-5}[/tex]
=-5
Find the quotient.
2^3/2^-1
Answers
Answer:
-4
Step-by-step explanation:
2^3 = 2 * 2 * 2 = 8
2^-1 = -2 = -2
2^3/2^-1 = 8/-2
=> 4/-1
=> -4
Hope it helps :)
Answer:
2^4 (or) 16
Step-by-step explanation:
2^3=2×2×2=8
2^-1 = 1/2
2^3/2^-1 = 8/(1/2) = 8×2 = 16
alternative method:
2^3/2^-1 = 2^(3-(-1))
= 2^(3+1)
= 2^4
= 16
please answer thank you
Answers
Answer:
1536 m²
Step-by-step explanation:
To find the area of the lateral faces, calculate the height of a lateral face first.
The height of a lateral face = S
The blue triangle is right-angled, so we can use Pythagoras Theorem to find S.
[tex] \sqrt{ {h}^{2} + {0.5b}^{2} } [/tex]
[tex] = \sqrt{ {16}^{2} + {12}^{2} } [/tex]
[tex] = \sqrt{400} [/tex]
= 20 m
Total surface area of a pyramid
= total surface area of lateral faces + base area
Area of 1 lateral face
= (base × height) ÷ 2
= (24×20)÷2
= 240 m²
Total surface area of the pyramid
= 240×4 + 24×24
= 1536 m²
What is the value of X?
Answers
Answer:
The answer is 46'
Step-by-step explanation:
The first triangle is:85'+53'+Y=180' so y=42'
The second triangle with X is:92+42'+X=180' so X=46'
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Find the simple interest earned, to the nearest cent, for the principal, interest rate, and time.
$650, 5%, 1 year
Help
Answers
Answer:
32.5
Step-by-step explanation:
I=Prt
I= 650*0.05*1
I=32.5
Keiko brought $51.75 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1/6 as much as the sketchbook, and the sketchbook cost 3/4 the cost of the paint set. Keiko had $3.00 left over after buying these items.
What was the cost of each item?
Answers
Step-by-step explanation:
[(1/6 × 3/4) + (3/4) + 1] n = 51.75 -3
(⅛ + ¾ +1)n = 48.75
15/8 n = 48.75
1.875 n = 48.75
n = 48.75/1.875
n = 26
so, the cost of :
the brush = ⅛×26 = $ 3.25
the sketchbook = ¾×26 = $ 19.5
the pain set = $ 26
Find the perimeter of the figure.
1 in
1 in
5 in
3 in
3 in
PLEASE HURRY ITS URGENT
Answers
Answer: My teacher told me to use 180 and divide something.
Step-by-step explanation:
Answer:
isnt itjust 15?
Step-by-step explanation:
1 +1+1+1 = 4 5+3+3 = 11 then 11+4 = 15 if this is incorrect im sorry
PLZ HELP ASAP
The white triangle drawn on the road sign in the picture has a height of 8 and a base of 5 which formula would be correct to find the area of this triangle
1) A= 1/2 (8) (5)
2) A=2(8)+2(5)
3) A=1/2(8+8)(5+5)
4) A=2(8)(8)+2(5)(5)
Answers
Answer:
[tex]\text{1) }\frac{1}{2}(8)(5)[/tex]
Step-by-step explanation:
The area of a triangle with base [tex]b[/tex] and height [tex]h[/tex] is equal to [tex]A=\frac{1}{2}bh[/tex]. Since we're given a base of 5 and a height of 8, the area is given by [tex]\boxed{\text{1) }\frac{1}{2}(8)(5)}[/tex].
Jared bought a new amplifier for his guitar by borrowing the money from his mom. The amplifier cost $235. Jared is paying his mom back $18 each week. If Jared still owes his mom $73, how many weeks has he been paying her back?
Answers
Answer:
9 weeks
235 -73=162 (this is the amount he paid)
162/18=9 (he has been paying his mom for 9 weeks)
Answer:
9 weeks
Step-by-step explanation:
235-73 = 162 (how much he has paid her thus far)
162/18 (how many times he payed her) = 9
Step 5: Mathematics Problem 10 of 10 Question: The variables x and y are directly proportional, and y = 4 when = 3. What is the value of y when 15? А. B. 12 C16 D. 20 E. I don't know d O ype here to search
Answers
Step-by-step explanation:
y=kx
4=k*3,4=3k,4/3=k.to find y when X is 15 ,y=kx,y=4/3*15=60/3=20
A car that is normally $4200 is on sale for 80% of its original cost.
what is the sale price of the car?
Answers
Answer:
$3360
Step-by-step explanation:
4200(.80) = 3360
anything less than 1.00 will be a decreasing amount, so i just took the 80% and put it as a decimal and multiplied to find the current cost of the car
If JK is formed by J(-7,-8) & K(1,4), determine if L(-9,5), lies on the perpendicular bisector.
Part A: What elements do you you need to know to confirm that Point L is on the perpendicular bisector of JK?
Part B: Find the elements you described in Part A , explain your work.
Part C: Verify if Point L is on the perpendicular bisector of JK. Justify your conclusion.
Answers
Answer:
Following are the responses to the given question:
Step-by-step explanation:
For point a:
Bisector Theorem: When a point has been on the perpendicular bisector of a segment, the perpendicular bisector is equivalent towards the segment endpoints. They understand that conversation also valid in addition to the Theorem including its perpendicular bisector. So the distance b/w L and J, L, and k must be found. Examine it then.
For point b:
Calculating the distance among two point:
[tex]d_0 = \sqrt{(x_1-x_2)^2 +(y_1-y_2)^2}[/tex]
Calculating the distance among J and L
[tex]d_1 = \sqrt{((-9)-(-7))^2 + (5)-(-8))^2}[/tex]
[tex]=\sqrt{(-2)^2+(13)^2}\\\\ = \sqrt{173}[/tex]
Calculating the distance among K and L
[tex]d_2 = \sqrt{((-9)-(1))^2 + (5)-(4))^2}[/tex]
[tex]=\sqrt{(10)^2+(1)^2}\\ = \sqrt{101}[/tex]
For point c:
As these two distances are not equal, L doesn't really lie on the JK bisector.
please help! (listing BRAINLIST and giving points)
Answers
Answer:
Step-by-step explanation:
sin x = opposite / hypotenuse
sin x = b / c
cos x = adjacent / hypotenuse
cos x = a / c
tan x = opposite / adjacent
tan x = b / a
01 1 point If a customer spends more than $20, he receives a 10% discount on his total bill: What does a customer whose bill is $80 /pay?
Answers
Answer:
try 40%
Step-by-step explanation:
In a triangle ABC, let G denote its centroid and let M,N be points in the interiors of the segments AB,AC, respectively, such that M,G,N are collinear. If r denotes the ratio of the area of triangle AMN to the area of ABC then find r.
Answers
Answer: hello options related to your question is missing attached below is the missing option
answer :
4/9 ≤ r < 1/2 ----- ( c )
Step-by-step explanation:
Given that G denotes the centroid of triangle ABC and points M, N are points found in the interiors of segments AB,AC
also Given that r denotes ratio of triangles AMN to triangle ABC
attached below is a detailed solution
When do creative people get their best ideas? USA Today did a survey of 966 inventors (who hold U.S. patents) and obtained the following information.
Time of Day When Best Ideas Occur
Time Number of Inventors
6 A.M.-12 noon 271
12 noon-6 P.M. 123
6 P.M.-12 midnight 327
12 midnight-6 A.M. 245
Required:
a. Assuming that the time interval includes the left limit and all the times up to but not including the right limit, estimate the probability that an inventor has a best idea during each time interval: from 6 A.M. to 12 noon, from 12 noon to 6 P.M., from 6 P.M. to 12 midnight, from 12 midnight to 6 A.M.
b. Do the probabilities add up to 1? Why should they?
Answers
Answer:
a.
0.2805 = 28.05% probability that an inventor has a best idea from 6 A.M. to 12 noon.
0.1273 = 12.73% probability that an inventor has a best idea from 12 noon to 6 P.M.
0.3385 = 33.85% probability that an inventor has a best idea from 6 P.M. to 12 midnight.
0.2536 = 25.36% probability that an inventor has a best idea from 12 midnight to 6 A.M.
b. They do, as the the sum of the probabilities of all possible outcomes should be 1, as is in this question.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the total outcomes.
We have:
A total of 966 inventors.
Question a:
6 A.M. to 12 noon
271 out of 966, so:
[tex]p = \frac{271}{966} = 0.2805[/tex]
0.2805 = 28.05% probability that an inventor has a best idea from 6 A.M. to 12 noon.
12 noon to 6 P.M.
123 out of 966, so:
[tex]p = \frac{123}{966} = 0.1273[/tex]
0.1273 = 12.73% probability that an inventor has a best idea from 12 noon to 6 P.M.
6 P.M. to 12 midnight
327 out of 966, so:
[tex]p = \frac{327}{966} = 0.3385[/tex]
0.3385 = 33.85% probability that an inventor has a best idea from 6 P.M. to 12 midnight.
12 midnight to 6 A.M.
245 out of 966. So
[tex]p = \frac{245}{966} = 0.2536[/tex]
0.2536 = 25.36% probability that an inventor has a best idea from 12 midnight to 6 A.M.
b. Do the probabilities add up to 1? Why should they?
0.2805 + 0.1273 + 0.3385 + 0.2536 = 1
They do, as the the sum of the probabilities of all possible outcomes should be 1, as is in this question.
I need help seeing what I did wrong
Answers
Answer: The two roots are x = 3/2 and x = -2
=========================================================
Explanation:
You have the right idea so far. But the two numbers should be 3 and -4 since
3*(-4) = -123+(-4) = -1The -1 being the coefficient of the x term.
This means you need to change the -3x and 4x to 3x and -4x respectively. The other inner boxes are correct.
---------
Refer to the diagram below to see one way to fill out the box method, and that helps determine the factorization.
If we place a 2x to the left of -2x^2, then we need an -x up top because 2x*(-x) = -2x^2
Then based on that outer 2x, we need a -2 up top over the -4x. That way we get 2x*(-2) = -4x
So we have the factor -x-2 along the top
The last thing missing is the -3 to the left of 3x. Note how -3*(-x) = 3x in the left corner and -3*(-2) = 6 in the lower right corner.
We have the factor 2x-3 along the left side.
---------
The two factors are (2x-3) and (-x-2) which leads to the factorization (x+3)(-x+2)
The last thing to do is set each factor equal to 0 and solve for x
2x-3 = 0 solves to x = 3/2 = 1.5-x-2 = 0 solves to x = -2The two roots are x = 3/2 and x = -2
Identify horizontal or vertical compression stretch of the function g(x) = 6x
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Answer:
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