a building is 16m from a television tower. From the top of the building, the angle of depression from the base 43 degrees, and the angle of elevation to the top of the tower is 24 degrees. Find the height of the tower?
2 answers
is it 4.18? please teach me how to answer this...:(
I made a sketch, letting the top of the building A
I drew in the tower, called the top P and the bottom Q
I drew a line from A to B, AB parallel to the ground
thus QB = 16 , the same height as the building.
We now have two right angled triangles, ABP and ABQ
in triangle ABQ, tan 43° = 16/AB
AB = 16/tan43
in triangle ABP, tan 24 = BP/AB
BP = ABtan24
= (16/tan43)(tan24) = 7.639..
so the height of the tower = 16 + BP = 23.639.. m
I drew in the tower, called the top P and the bottom Q
I drew a line from A to B, AB parallel to the ground
thus QB = 16 , the same height as the building.
We now have two right angled triangles, ABP and ABQ
in triangle ABQ, tan 43° = 16/AB
AB = 16/tan43
in triangle ABP, tan 24 = BP/AB
BP = ABtan24
= (16/tan43)(tan24) = 7.639..
so the height of the tower = 16 + BP = 23.639.. m
2 answers