In triangle abc, measure of angle a = 90 degrees and line an is an altitude. if ab = 20 in. and ac = 15 in., find bc, bn, nc, an
Answers
Answer:
BC = 25 in
AN = 12 in
BN = 16 in
NC = 9 in
Formulas:
Pythagorean Theorem
[tex]c^2 = a^2 + b^2[/tex]
c ... hypotenuse
a ... one leg
b ... another leg
Pythagorean theorem is used in right triangles (triangles in which one angle is 90°).
Area of triangle
[tex]A = \frac{1}{2}bh[/tex]
A ... area of triangle
b ... base (one of the sides of the triangle)
h ... height perpendicular to base
Step-by-step explanation:
Given:
A = 90°
AB = 20 in
AC = 15 in
See attached picture.
1) BC
To find BC we can use Pythagorean theorem, since ABC is a right triangle. We have the lengths of two legs (AB, AC) and we are finding the hypotenuse.
[tex]c^2 = a^2 + b^2\\\text{BC}^2 = \text{AB}^2 + \text{AC}^2\\\text{BC}^2 = 20^2 + 15^2\\\text{BC}^2 = 625\\\sqrt{\text{BC}^2} = \sqrt{625}\\\text{BC} = 25 \text{ in}[/tex]
2) AN
AN is the height corresponding to base BC. To find it we can use formula for the area of the triangle. But first let's find the area of the triangle.
Notice how AB is perpendicular to AC. We can use AB as base and AC as height.
[tex]A = \frac{1}{2}bh\\\\A = \frac{1}{2} \times \text{AB} \times \text{AC}\\\\A = \frac{1}{2} \times 20 \times 15\\\\A = 150 \text{ in}^2[/tex]
Now that we have area, we can use BC as base and AN as height and solve for AN.
[tex]A = \frac{1}{2}bh\\\\A = \frac{1}{2} \times \text{BC} \times \text{AN}\\\\150 = \frac{1}{2} \times 25 \times \text{AN}\\\\\ 300 = 25 \times \text{AN}\\\\12 = \text{AN}\\\\\text{AN} = 12 \text{ in}[/tex]
3) BN
Let's use Pythagorean theorem in right triangle ABN. Hypotenuse is AB.
[tex]c^2 = a^2 + b^2\\\text{AB}^2 = \text{AN}^2 + \text{BN}^2\\20^2 = 12^2 + \text{BN}^2\\400 = 144 + \text{BN}^2\\256 = \text{BN}^2\\\sqrt{256} = \sqrt{\text{BN}^2}\\16 \text{ in} = \text{BN}[/tex]
4) NC
We know the lengths of BC an BN, so we can just subtract.
[tex]\text{NC} = \text{BC} - \text{BN}\\\text{NC} = 25 - 16\\\text{NC} = 9 \text{ in}[/tex]
Related Questions
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Answer:
its 90
Step-by-step explanation: multiply it 6 by 14 feet, than add 6.
6*14=84+6=90
Answer:
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Step-by-step explanation:
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Which values represent solutions to cos
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Step-by-step explanation:
18. Find the area of each regular polygon. Round your answer to the nearest tenth if necessary.
19. Use the information provided to write the equation of each circle.
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22. 23. Find the value of each trigonometric ratio.
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Answer:
Step-by-step explanation:
If Maggie invests 16,250 at a rate of 4.9%, compounded monthly, find the value of the investment after 7 years.
Answers
Answer:
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Step-by-step explanation:
Principal Amount ( P ) = $16250
Interest Rate ( r ) = 4.9% or 0.049( divide by 100)
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A = P ( 1 + r/n)^nt
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Substitute the given values of P, r, n and t to the formula for the compound interest.
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What is the constant of proportionality between y and a in the graph below?
2
10
1 2 3 4 5 6 7 8 9 10
86
7
6
5
4
3
2
1
0
Xeno
X
1/2
21/3
|
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Answers
The constant of proportionality between y and x in the graph is 3/2 option third is correct.
What is a proportional relationship?It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.
We have a graph shown in the picture.
As we can see, the given graph shows a line, which passes through (0, 0)
y = ax
a is the constant of proportionality.
We have two points (0, 0) and (6, 9) (from the graph)
From the above two points, we can find the equation of a line.
y = (9/6)x
y = (3/2)x
The value of the constant of proportionality is 3/2
Thus, the constant of proportionality between y and x in the graph is 3/2 option third is correct.
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Solve the equation using square roots: x2 -81=0
Answers
Hi Student!
This question is pretty straight-forward because it is asking for us to solve to equation using square roots. We don't need to find any important information as this problem is pretty simple. We just need to use some algebra to move numbers around and we will get our answer.
Add 81 to both sides
[tex]x^2 - 81 = 0[/tex][tex]x^2 - 81 + 81 = 0 + 81[/tex][tex]x^2 = 81[/tex]Square root both sides
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2
Write you
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Answers
Answer:
5
Step-by-step explanation:
→ The radius is square root of the last number which is usually denoted by r² in the format ( x - a )² + ( y - b )² = r²
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Answers
Muscular Endurance - The ability of a skeletal muscle or group of muscles to continue contracting over a long period.
Step-by-step explanation:
I hope it'll help you...
Answer:
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Step-by-step explanation:
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Answer:
monomial
Step-by-step explanation:
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According to a recent survey, it is known that 90% of people enjoy disney movies, 70% of
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Answers
Answer:
[tex]P(\text{Disney}| \text{Pixar})\approx0.929[/tex]
Step-by-step explanation:
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Answer:
Step-by-step explanation:
12P3 = 12! / (12-3)!
= 12*11*10
= 1320.
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= 8.
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Answers
Answer:
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Step-by-step explanation:
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Can someone please answer this, ill give you brainliest Would be very appreciated.
Answers
Explanation:
f(x) = (x-4)(x+2)
1) For x-intercept, y will be 0
(x-4)(x+2) = 0(x-4) =0, (x+2) = 0x = 4, x = -2x-intercept: (4, 0), (-2, 0)
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Quadratic function:
(x-4)(x+2)x² +2x-4x -8x² -2x -8vertex:
x = -(-2)/2(1)x = 1y: (x-4)(x+2) = (1-4)(1+2) = -9
ordered pair of vertex: (1, -9)
3) For y-intercept, x will be 0
(x-4)(x+2)(0-4)(0+2)-8y-intercept: (0, -8)
Answer:
(4, 0) and (-2, 0)(1, -9)(0, -8)Step-by-step explanation:
Q1 : Finding x-intercepts
Take f(x) to be 0, because the intercepts lie on the x-axis0 = (x - 4)(x + 2)x = 4 and x = -2The x-intercepts are : (4, 0) and (-2, 0)Q2
Coordinates of vertex are : (h, k)Expand the polynomialx² - 2x - 8h = -b/2a = 2/2 = 1k = -D/4aD = b² - 4ac = 4 - 4(1)(-8) = 4 + 32 = 36k = -36/4 = -9The vertex is : (1, -9)Q3
Take x = 0y = 0² - 2(0) - 8y = -8y-intercept is : (0, -8)Based on the data in the box plots, what is the best evidence to show which diver had greater overall success during the meets so far this season? ani was more successful because she had an outlier. marta was more successful because she received the highest score. ani was more successful because she had the greater measure of center. marta was more successful because she had the greater total spread.
Answers
The best evidence to show which diver had greater overall success is Marta was more successful because she had the greater total spread.
What is a box plot?Box Diagram provides a quick visual summary of the variability of values in a dataset. They show the median values, upper and lower quartiles, minimum and maximum values, and any outliers in the dataset.
In this case, the total spread of Ani is from 4.5 to 9.5 and the total spread of Marta is from 4 to 10, we can conclude that Marta was more successful than Ani because of greater total spread.
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Richard takes a hang gliding lesson. He
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downward for the first 5 minutes.
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for 10 minutes. The last 3 minutes
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Answer:
it a nice graph I made
Step-by-step explanation:
yeah just click the image
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Q, Z, W, R, N
what's the graph of y=3x-5
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Answer:
Step-by-step explanation:
Need help:
Find the distance between A
and B
Answers
Answer:
2.6
Step-by-step explanation:
A= -1.3
B=1.3
1.3--1.3=2.6
Answer:
2.6 units
Step-by-step explanation:
If you round down the distance is 2. then you all the 2 decimals 0.3 and 0.3 to get 2.6 units.
Luca shows his work in finding the solution to 2−6=5−5(−1)
. After checking his answer in the original equation, he found that it did not work. Where did he make a mistake?
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Answers
The coordinates of the image of (-3, -7) after the translation will be equal to .(-12,2)
What is translation?The process of changing the location of the image on the coordinate system will be known as the translation. Here the image is translated as (x-9,y+9).
The given coordinate of the point is:- (-3,-7)
So the translation will be calculated as:-
=(x-9,y+9 )
=(-3-9,-7+9
=(-12,2)
Hence coordinates of the image of (-3, -7) after the translation will be equal to (-12,7)
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I need some help with these please :')
Answers
Step-by-step explanation:
problem 1.
1. 6y = 30
2. y = 5
3. 3x + 2(5) = 16
4. 3x+10=16
5. 3x=6
6. x=2
solution: (2,5)
problem 2.
1. x=7
2. 4(2)-2y=18
3. 28-2y=18
4. -2y= -10
5. y=5
solution (7,5)
problem 3
10x=10
x=1
7(1) +y =-2
y=-9
(1,9)
problem 4
0= -6
no solution
problem 5
0=0
Infinite many
Which inequality represents the given situation? No more than 47 beds are in the hospital.
beds in the hospital > 47
beds in the hospital < 47
beds in the hospital ≤ 47
beds in the hospital ≥ 47
Answers
Answer:
beds in the hospital ≤ 47
Step-by-step explanation:
No more 47 means not greater than 47.
But can be = to 47 or less than it.
In your opinion, what components of a free market are the most important
Answers
A free market is one where voluntary exchange and the laws of supply and demand provide the sole basis for the economic system, without government intervention. A key feature of free markets is the absence of coerced (forced) transactions or conditions on transactions.
GIVING BEAINLIESTTTTTTT!!!!!!!!!Find the measure of
Answers
Answer:
134°Step-by-step explanation:
Angles 1 and 3 form a linear pair so they sum to 180°.
m∠1 + m∠3 = 180°Substitute the values and solve for x
8x + 6 + 2x + 14 = 18010x + 20 = 18010x = 160x = 16Find the measure of ∠1
m∠1 = 8*16 + 6 = 13410 times as much as 0.71
Answers
Answer:
7.1
Step-by-step explanation:
if we put this into a number sentence it will be 0.71*10 which is 7.1
You know that 3 pencils and 7 pens cost $24, while 3 pencils and 3 pens cost S12.
How many dollars are 4 pencils and 5 pens worth?
Answers
Answer:
5 pens = 15$ and 4 pencils = 4$
Step-by-step explanation:
7-3=4, so 4 pens is 12$
12/4 = 3, so 1 pen = 3$
Remove the pens from the equation
7x3=21
24-21=3
3/3=1, so each pencil costs 1$
4 pencils and 5 pens are worth $23.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
Let the cost of one pencil be x, and the cost of one pen be y.
Then we can set up the following system of equations based on the given information:
3x + 7y = 24 ...(1)
3x + 3y = 12 ...(2)
Solving these two equations, we can find that x = 2 and y = 3.
Now, we can use these values to find the cost of 4 pencils and 5 pens:
4x + 5y = 4(2) + 5(3) = 8 + 15 = $23
Therefore,
4 pencils and 5 pens are worth $23.
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PLS HELP!!
What is the measure of ZXYZ?
A. 63°
B. 54°
C. 252°
D. 126°
Answers
Geometry, need help asap please
Answers
Answer: 15.01
Step-by-step explanation: