Question

Malaya is standing between a 99-foot talk courthouse and 54-ft y’all bank. If the angle of elevation from the point where Malaya is standing to the top of the courthouse is 72, while the angle of elevation to the top of the bank is 35. What is the distance between the courthouse and the bank?

Answer 1

The distance between the courthouse and the bank = 109.29 ( to 2 decimal places )

Explanation:

from the diagram, there are two right-angled triangle,

taking the right-angled triangle on the left:

Tan θ =
`(Opposite)/(Adjacent)`

where:

θ = 72°

Opposite = 99 Ft.

Adjacent = x

∴ Tan 72 =
`(99)/(x)`

3.0777 =
`(99)/(x)`

∴
`x` =
`(99)/(3.0777)` = 32.167

considering the right-angled triangle on the right

Tan θ =
`(Opposite)/(Adjacent)`

where :

θ = 35°

Opposite = 54 Ft.

Adjacent = y

∴ Tan 35 =
`(54)/(y)`

0.7002 =
`(54)/(y)`

∴
`y` =
`(54)/(0.7002)`

`y` = 77.121

Therefore, distance between courthouse and bank = x + y

= 32.167 + 77.121 = 109.29 Ft.