Help for a Long question. Year 9 work.

Question

Two building are 20 metres apart. The angle of elevation from the top of the smaller building to the top of the taller building is 20 degrees. The angle of depression from the top of the smaller building to the base of the taller building is 45 degrees. What is the height of the taller building

Answer 1

Draw a fig

 

First we will find the height of small building

 

let consider

 

small building height =x

 

tan 45 = x/20

 

x= tan 45 * 20

 

x= 20

 

Now for  large building

 

large building height = x+ y

 

tan 20 = y /20

 

y= tan 20 * 20

 

y = 7.28

 

large building height = x+ y= 20 + 7.28=27.28 meters