# Thread: Trigonometry Word Problem ... Question 2

1. ## Trigonometry Word Problem ... Question 2

The following questions are for a final class project. Obviously these questions are very hard, and I am unsure how to completely answer these with the proper and complete work shown. Help on answering these questions with work/ steps would be greatly appreciated.

7. The angle of depression from the top of a tall building to the roof of a shorter building is 48°. The smaller building is 16m tall and the buildings are 30m apart. How high is the taller building?

8. Two fire towers are 575m apart. The first tower is 200m high and the second is 350m high. What is the angle of depression from the top of the second tower to the top of the first?

7. The angle of depression from the top of a tall building to the roof of a shorter building is 48°. The smaller building is 16m tall and the buildings are 30m apart. How high is the taller building?
Code:
____
|  |* * * * * * * * *
|  |    * 48        *
|  |        *       * x
|  |            *   *
|  |                *____
|  |                 |  |
|  |                 |  |
|  |                 |  | 16 m
|  |                 |  |
|  |                 |  |
|--|-----------------|--|
30 m
If you can see the right triangle I attempted to draw above, we know that the adjacent side is 30 and the angle is 48 deg. We want to find the length of the opposite side:
\begin{aligned}
\tan 48^\circ &= \frac{x}{30} \\
30\tan 48^\circ &= x \\
x &\approx 33.32
\end{aligned}

Add that to 16 m to get the height of the taller building:
$33.32 + 16 \approx 49.32$
The height of the taller building is about 49.32 m.

01

8. Two fire towers are 575m apart. The first tower is 200m high and the second is 350m high. What is the angle of depression from the top of the second tower to the top of the first?
This is the same type of problem as #7, except what is known is different:
Code:
      ____
|  |* * * * * * * * *
|  |    * x         *
|  |        *       *
|  |            *   *
|  |                *____
350 m |  |                 |  |
|  |                 |  |
|  |                 |  | 200 m
|  |                 |  |
|  |                 |  |
|--|-----------------|--|
575 m
You know the adjacent side of this triangle, and you know the opposite side. (Can you see what it is?) So use the same tangent ratio, but now, the unknown is the angle.

01

4. "You know the adjacent side of this triangle, and you know the opposite side. (Can you see what it is?)"

Taller Building - Smaller Building = 350 - 200 = 150

Got my angle of depression at 15 degrees.

Thanks very much for the help.