Question

From a ship, the angle of elevation of a point, A, at the top of a cliff is 21°. After the ship has sailed 2,500 feet directly toward the foot of the cliff, the angle of elevation of ∠A is 47°. (Assume the cliff is perpendicular to the ground.) The height of the cliff is __ feet.

Answer 1

1495ft

Explanation:

your welcome

Answer 2

10701.97 feet.

Explanation:

Refer the attached figure

The angle of elevation of a point, A, at the top of a cliff is 21° i.e. ∠ACB = 21°

The ship has sailed 2,500 feet directly toward the foot of the cliff i.e. CD = 2500 feet.

Then the angle of elevation becomes 47° i.e.∠ADB = 47°

Let BD be x

So, BC = BD+DC=x+2500

Let the height of the cliff be h feet.

In ΔABD

We will use trigonometric ratios

`tan\theta = (Perpendicular)/(Base)`

`tan47^(\circ) = (AB)/(BD)`

`1.072= (h)/(x)`

`1.072x=h` ---a

In ΔABC

We will use trigonometric ratios

`tan\theta = (Perpendicular)/(Base)`

`tan21^(\circ) = (AB)/(BC)`

`0.869 = (h)/(x+2500)`

`0.869(x+2500) =h`

`0.869x+2172.5 =h` -----b

Equate a and b

`0.869x+2172.5 =1.072x`

`2172.5 =1.072x-0.869x`

`2172.5 =0.203x`

`(2172.5)/(0.203)=x`

`10701.97=x`

Thus the height of the cliff is 10701.97 feet.