Paul is standing on a 39 m high building. The angle of elevation to the top of a taller building is 47 degrees and the angle of depression to the bottom of the same building is 36 degrees. What is the height of the taller building to the nearest tenth.
Draw a diagram and review your basic trig functions. Then it will be clear that if the distance between the buildings is x and the height of the taller building is h, then
39/x = tan36°
(h-39)/x = tan47°
so,
h = (39/tan36°)(tan 47°) + 39
That's what is difficult for me. I have trouble drawing the diagram. Otherwise I know how to solve these problems. I need help drawing diagrams of these word problems. Is there a way you can possibly teach me how to draw diagrams?
In this case,
Draw the horizontal ground
Draw two vertical lines standing on the horizontal ground, one taller than the other. Label their tops A and B, and their bottoms C and D
Draw a horizontal line from the top of the shorter building (A) to where it intersects with the taller building at E.
The distance x between the buildings is x = AE = CD
Draw the sloping lines AB and AD. Label the angles DAE and EAB as required.
Now you can see the required trig relationships, since
DE = 39
EB = h-39
There is no trick to drawing diagrams. Just take each sentence and turn it into line segments.
To find the height of the taller building, we can use the concept of trigonometry. Given the information, we have two right triangles: one formed by Paul, the taller building's top, and the top of the 39 m building, and another formed by Paul, the base of the 39 m building, and the taller building's bottom.
Let's find the height of the taller building step by step:
1. First, let's calculate the distance from Paul to the 39 m building's top. We can use the tangent function in trigonometry, which is defined as the opposite side divided by the adjacent side of a right triangle. In this case, the opposite side is the height of the 39 m building (39 m) and the adjacent side is the distance from Paul to the 39 m building's top (let's call it x):
tan(47°) = 39 m / x
2. Rearranging the equation, we get:
x = 39 m / tan(47°)
Use a calculator to find the value of tan(47°), which is approximately 1.0724. Therefore:
x = 39 m / 1.0724
x ≈ 36.37 m
So, the distance from Paul to the 39 m building's top is approximately 36.37 m.
3. Now, let's find the distance from Paul to the taller building's bottom. Again, we'll use the tangent function:
tan(36°) = height of the taller building / x
Substituting the known value of x as 36.37 m, we can solve for the height of the taller building:
height of the taller building = tan(36°) * 36.37 m
Use a calculator to find the value of tan(36°), which is approximately 0.7265. Therefore:
height of the taller building ≈ 0.7265 * 36.37 m
height of the taller building ≈ 26.41 m
So, the height of the taller building is approximately 26.41 m to the nearest tenth.