Question

Sameena measures the angle from the ground to the top of a building from two locations. The angle of elevation from the first point is 45°, and the angle of elevation from the second point is 60°. The distance from the second point to the top of the building is 150 ft.What is the distance from the first observation point to the top of the tower (x)? Round the answer to the nearest tenth.

Answer 1

B. 183.7 ft

Explanation:

Answer 2

183.710 feet

Explanation:

The angle of elevation from the first point to the top of the building is 45° i.e.∠ABD = 45°

The angle of elevation from the second point to the top of the building is 60° i.e.∠ACD = 60°

The distance from the second point to the top of the building is 150 ft i.e.AC = 150 feet

We are supposed to find the distance from the first observation point to the top of the tower i.e.AB = x

In ΔACD

`Sin \theta = (Perpendicular)/(Hypotenuse)`

`Sin 60^(\circ) = (AD)/(AC)`

`(√(3))/(2) = (AD)/(150)`

`(√(3))/(2) * 150 =AD`

`129.903 =AD`

In ΔABD

`Sin \theta = (Perpendicular)/(Hypotenuse)`

`Sin 45^(\circ) = (AD)/(AB)`

`(1)/(√(2))= (129.903)/(AB)`

`AB= (129.903)/((1)/(√(2)))`

`AB= 183.710`

Hence the distance from the first observation point to the top of the tower is 183.710 feet