A surveyor is trying to find the length of a lake. He finds a baseline distance AB of 125 m. Angle A is measured to be 41.6° and angle B is measured at 124.3°. Find the length of the lake d. Please and Thank you.
Answers
Answer:
[tex]d = 340.7m[/tex]
Step-by-step explanation:
See attachment for question illustration
From the attachment, we have:
[tex]AB = 125m[/tex]
[tex]<A = 41.6[/tex]
[tex]<B = 124.3[/tex]
Required
Solve d
First, we need to calculate <C
[tex]<A + <B + <C = 180[/tex] --- angles in a triangle
[tex]41.6+ 124.3 + <C = 180[/tex]
[tex]165.9+ <C = 180[/tex]
Make <C the subject
[tex]<C = 180 - 165.9[/tex]
[tex]<C = 14.1[/tex]
Next, we apply Sine's law to solve for d
[tex]\frac{A}{Sin\ A} = \frac{B}{Sin\ B} =\frac{C}{Sin\ C}[/tex]
In this case:
[tex]\frac{d}{Sin\ 41.6} = \frac{125}{Sin\ 14.1}[/tex]
Make d the subject
[tex]d = \frac{125 * sin\ 41.6}{sin 14.1}[/tex]
[tex]d = \frac{125 * 0.66392621265}{0.24361501178}[/tex]
[tex]d = \frac{82.9907765812}{0.24361501178}[/tex]
[tex]d = 340.663639629[/tex]
[tex]d = 340.7m[/tex]
Hence, the base of the lake is approximately 340.7m
Related Questions
Find the difference.
(-29+7) – (9+11) = 0
Answers
Answer:
Step-by-step explanation:
lets remove the parenthesis
-29+7-9-11=-42
Answer:
-42
Step-by-step explanation:
(-29+7)= -22
(9+11) = 20
-22-20= -42
Can somebody help me ??
Answers
Answer:
y = 98
z = 21
Step-by-step explanation:
in the picture, y and 82 are supplementary angles because the are same side interior angles. This means that we can create this equation:
y = 180 - 82
we get y = 98
<Y and <4z + 14 are vertical angles, so we can also say that they are equal to each other. So we can create this equation:
4z + 14 = 98
subtract 14 from both sides:
4z = 84
divide both side by 4 to find z:
z = 21
Answer:
y = 82
z = 21
Step-by-step explanation:
You can get y almost immediately.
82 and y are supplementary. Interior angles on the same side of the transversal = 180
82 + y = 180 Subtract 82 from both sides
y = 180 - 82
y = 98
y and 4z + 14 are equal.
y = 4z + 14 Substitute for y
98 = 4z + 14 Subtract 14 from both sides.
98-14 = 4z
84 = 4z Divide by 4
84/4 = 4z/4
21 = z
Which of the following expressions is equal to -3x^2-12?
Answers
Answer:
The answer is (-3X+6i)(x+2i)
Step-by-step explanation:
You can do this by plugging in the answers in the equations and get that (-3x+6i)(x+2i) equals the following expression.
You’ve learned to identify whether a function is even or odd both graphically and algebraically. How does the notation for reflections over the x-axis and over the y-axis relate to the notation for even and odd functions? Remember that if f(-x) = f(x), a function is even, and if f(-x) = -f(x), then the function is odd.
Answers
Answer:
Because even and odd are 2 different ways to determine whether or not you get the right answer for the chosen function.
Step-by-step explanation:
Hope this helps!!!
Answer:
For even functions, we take f(-x) to be the starting function. The y-axis reflection of this function is f(-(-x)), which is equal tof(x). So the relationship f(-x) = f(x) means that the function is the same as its y-axis reflection.
For odd functions, there are two reflections that must occur. First, we start with f(-x). The y-axis reflection of this function is f(-(-x)) = f(x). When we apply an x-axis reflection to this result, we get -f(-(-x)) = -f(x). So the fact that f(-x) = -f(x) means that odd functions are the same as sequential reflections across both the x-axis and the y-axis. (The same sequence of reflections also represents a rotation 180 degrees about the origin).
Step-by-step explanation:
Solve for x. Triangles below are similar.
a) 13
b) 10
c) 4
d) 3
Answers
Answer:
the answer is 4 (option C)
Step-by-step explanation:
Since the triangles are similar, and in triangle UTV both sides are equal, we can consider QTR also has two equal sides.
therefore, the equation forms:
13x + 3 = 55
13x = 55 - 3
13x = 52
x = 52/13
x = 4
Which of the following is closest to 1?
9/8
11/10
10/9
4/5
6/7
Answers
Help please help I’ll give brainliest
Answers
Answer:
108
Step-by-step explanation:
======================================
Explanation:
Rotate the arrow so that it is pointing up.
Draw a line separating the arrow into a triangle up top and a rectangle below that.
The rectangular portion has area of 6*4 = 24 square units.
-----------------
The triangular portion up to has area of
0.5*(base)*(height) = 0.5*(4+4+4)*(15-6) = 54
The base is 4+4+4 due to the '4's along the bottom of the triangle. The middle 4 might be the trickiest to spot, but keep in mind that rectangles have opposite sides that are the same length.
The height of the triangle is 15-6 since we start with an overall height of 15, and then subtract off 6 (which was the height of the rectangle).
-----------------
Once you know the areas of the triangle and rectangle, you add them up to get 54+24 = 78 square units.
The value 14 along the diagonal portions of the triangle isn't used. This information is probably put in to distract or trick students. However, if you needed to find the perimeter, then you will use the 14's.
What is quardtric form
Answers
Answer:
445
Step-by-step explanation:
For a Biology assignment, Lisa collected data on plant growth of a sunflower every week for 9 weeks. When Lisa first planted the sunflower, it was 10 centimeters tall. The time (in weeks) is plotted against the height (in centimeters) as shown below. Using the best-fit line, approximately how tall was the sunflower plant during the fifth week? 33 centimeters 34 centimeters 35 centimeters 30 centimeters
Answers
Answer:
I think it was 34 cm because it should be not too long
Step-by-step explanation:
this is from my logic perspective
Equivalent expressions
Which expressions are equivalent to 4(4a + 5) ?
Choose 3 answers:
16a + 5
16a + 20
12a + 20 + 4a
© 2(8a + 10)
© 16a +5+4
Answers
Answer:
16a + 20
12a + 20 + 4a
2(8a+10)
Step-by-step explanation:
45% of a number is 180
Answers
Step-by-step explanation:
45% of number = 180
=> 100% of number = 180 * (100/45) = 400.
Hence the number is 400.
"select all the numbers that are solutions to the equation x^3=27"
Answers
3^3 = 27
the cubed root of 27 is 3
The x = ∛27 and x = 3 are solution to the equation x³=27 option (B) and option (C) are correct.
What is a cube root?It is defined as the sum of two or more numbers. The original number is obtained by multiplying the cube root of a number three times; for example, the cube root of x is z.
We have equation:
x³ = 27
Taking cube root both side
∛x³ = ∛27
x = ∛27
x = 3
Thus, the x = ∛27 and x = 3 are solution to the equation x³=27 option (B) and option (C) are correct.
Learn more about the cube root here:
brainly.com/question/12726345
#SPJ2
15
0 23.7
O 25.9
0 27.5
0 29.5
Answers
Answer:
Bro just look up trig triangle calculator
Step-by-step explanation
Answer:
27.5
Step-by-step explanation:
sin(33) = 15/x
x=15/sin(33)
Gene paid a deposit on a leased car. The deposit earns 2.8 percent simple annual interest. At the end of the year, the interest that is earned is $22.40. What was the amount of the original deposit?
Answers
Answer:
The original amount was: P = $800
Step-by-step explanation:
Given
Interest I = $22.40
Interest rate = r = 2.8% = 0.028
time t = 1 year
Using the interest formula
I = Prt
I = InterestP = Principle or initial valuer = interest rate t = time (years)substituting the values
I = Prt
22.40 = P (0.028) (1) ∵ I = 22.40, r = 2.8% = 0.028, t = 1
P = 22.40 / 0.028
P = $800
Therefore, the original amount was: P = $800
it's D (800.00)
HAVE A NICE DAY
The two triangles are similar.
Solve for h.
Give an exact answer.
Answers
Answer:
4.5 m
Step-by-step explanation:
if the two triangles are similar than it would mean that zy to xy is same ratio to cb to ab which means that the second triangle is only enlarge version of the first triangle. so divide 7.2 by 1.6 and multiply 1 to get the solution of 4.5
Please help if possible due today thank you so so much!!
10points!❤️❤️❤️
A teacher asked her students how many pets they own. Here are the results:
Answers
The answer would be B. In the sequence;
0,0,1,1,1,1,2,2,2,3,4,4,8
Zero is mentioned twice, and if you take a glance at the other plots, they all have 3 dots above them, whereas answer choice B has 2 which is what we’re looking for.
Which of the following polnts is a solution of the Inequality y<-|x|?
(1,0)
(1,-2)
(1,-1)
Answers
Answer:
(1,-2)
Step-by-step explanation:
x = 1, y= -2
by sub.
-2<-1 so it's true
ERGENT! DUE TODAY! What is the equation in point-slope form of the line that passes through the point (3,-2) and has a slope of 2/3?
(look at image)
Answers
Answer:
y = 2/3x - 4
Step-by-step explanation:
neeeeddd helppp asap
Answers
The easy way to do it is Just divide 360 from 5 because that’s the amount of times you turn it ...
Maggie goes to a clothing store to shop for t-shirts. The store is having a sale on t-shirts for 25% off each shirt. She purchases 5 t-shirts that were regularly priced at $22. What was the total the store charged her with the discount, but before tax?
Answers
Because 22-5% x 5 is 109.75
Answer:
A
Step-by-step explanation:
Which statement(s) describe the graph of the equation x=-2? Select all that apply
Answers
Answer:
B, D.
Explanation:
When graphed out it is a vertical line. A vertical line has an undefined slope.
The x intercepts the line at (-2,0).
What is the volume of a cylinder, in cubic centimeters, with a height of 11 centimeters
and a base diameter of 6 centimeters? Round to the nearest tenths place
Answers
Answer: V = 311.0
Step-by-step explanation:
Formula: [tex]V = \pi r^2h[/tex]
[tex]V=\pi (3)^2 (11)[/tex]
[tex]V=99\pi[/tex]
V = 311.02
V = 311.0
Q15) 1.0 marks
Choose the missing term in the below series.
26, 37, 50, 65, 82, ?
Answers
Answer:
82
Step-by-step explanation:
Answer:
101
Step-by-step explanation:
from the first one to second one it goes up by 11 then 13 then 15 then 17 then 19
82+19=101
Q. Penelope is told to clean all the windows at her house. After cleaning 9 windows her job is
30% complete. How many windows does she clean in all?
Answers
Answer:
30
Step-by-step explanation:
Proportions!
Is this a function or not a function
Answers
Answer:
It is a function
Step-by-step explanation:
A function states that you must have one output every one input and this is done but with the same output.
Which of the following expressions is equivalent to the expression 42+90?
A. 6(7+14)
B.6(7+15)
C.7(6+12)
D.6(36+84)
Answers
6*7=42 and
6*15=90
Answer:
B
Step-by-step explanation:
42 + 90 = 132 > 6(7+15) > 6*22=132 > 6(7 + 15)= 132
Please help!! I have trouble in math and will give points and thanks for this!!
Answers
Answer:
-5
Step-by-step explanation:
You can count backwards from -1.
-1, -2, -3, -4, and then -5 is the blue dot.
The left side of 0 is the negative side. The right side is the positive side.
Hope this helps!
Answer:
-5
Step-by-step explanation:
If you're going backward on the number line then you are in the negative zone because of -1
2 L = _____ ml can someone help? :((
Answers
Answer:
2000
Step-by-step explanation:
Answer:
2000 ml
Step-by-step explanation:
Robert pays $32.04 for 6 student tickets to the basketball game. What is the cost of each student ticket?
Answers
Answer:
$5.34
Step-by-step explanation:
Step-by-step explanation:
$5.34
hope it helps!
......
Find the value of n.
2.8 ÷ n = 0.028
Answers
Answer:
100
Step-by-step explanation:
2.8/n = 0.028
2.8/0.028 = n
100 = n