Question

Two office buildings are 62 meters apart. The height of the taller building is 212 meters. The angel of depression from the top of the taller building is 15 degrees. Find the height of the shorter building to the nearest meter.

Answer 1

Answer:

The height of the shorter building is 195 meters

Step-by-step explanation:

The complete question is

Two office buildings are 62 meters apart. The height of the taller building is 212 meters. The angel of depression from the top of the taller building to the top of the shorter building is 15 degrees. Find the height of the shorter building to the nearest meter

see the attached figure to better understand the problem

step 1

In the right triangle EDC

Find the length ED

we know that

$tan(15^o)=\frac{ED}{DC}$ ----> by TOA ( opposite side divided by adjacent side)

substitute the given values

$tan(15^o)=\frac{ED}{62}$

$ED=tan(15^o)(62)=17\ m$

step 2

Find the height of the shorter building

Let

h ----> the height of the shorter building

we know that

$h=BC-ED$

substitute

$h=212-7=195\ m$