Question

HELP QUICKLY Christina and Youssef work in office buildings that are 80 feet away from each other. From the top of her office building, Christina notices that the angle of elevation to the top of Youssef’s building is 45°. The angle of depression from Christina to the base of Youssef’s building is 56°. Find the height of Youssef’s office building, rounded to the nearest tenth of a foot.

Answer 1

answer is 198.6

Explanation:

Answer 2

About 198.6 feet

Explanation:

This situation essentially forms a sideways triangle with height 80 feet. It can be divided into two right triangles, which you can each find the base length for, and then add them together to find the total height of the building.

Let's start with the lower base (with the angle measure of 56 degrees), which we'll call b. The tangent of an angle in a right triangle is the length of the opposite side divided by the length of the adjacent side, meaning that:

`\tan 56=(b)/(80) \\\\b=80 \cdot \tan 56\approx 118.6`

Now, let's do it for the upper part, which we'll call y:

`\tan 45=(y)/(80) \\\\y=\tan 45 \cdot 80=1 \cdot 80 =80`

Adding these together, you get a height of approximately 198.6 feet. Hope this helps!