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
[tex]tan(15^o)=\frac{ED}{DC}[/tex] ----> by TOA ( opposite side divided by adjacent side)
substitute the given values
[tex]tan(15^o)=\frac{ED}{62}[/tex]
[tex]ED=tan(15^o)(62)=17\ m[/tex]
step 2
Find the height of the shorter building
Let
h ----> the height of the shorter building
we know that
[tex]h=BC-ED[/tex]
substitute
[tex]h=212-7=195\ m[/tex]
