Question

The angle of depression from the top of a flag pole to a point on the ground is 30°. If the point on the ground is 75 feet from the base of the flag pole, how tall is the pole to the nearest foot? A) 38 feet B) 43 feet C) 53 feet D) 106 feet

Answer 1

B) 43 feet

Explanation:

Let AB represents the height of pole and C represents the point on the ground ( shown in the below diagram ),

We need to find : Measure of AB.

Since, angle of depression from the top of a flag pole to a point on the ground is 30°,

By the alternative interior angle theorem,

m∠ACB = 30°,

∵ m∠ABC = 90°,

By the trigonometric ratio,

`\tan 30^(\circ)=(AB)/(BC)`

We have BC = 75 ft,

`\tan 30^(\circ)=(AB)/(75)`

`(1)/(√(3)) = (AB)/(75)`

`\implies AB = (75)/(√(3))= 43.3012\approx 43`

Hence, the pole would be 43 ft tall ( approx )

Answer 2

Height of flag pole to the nearest foot is 43 feet

Explanation:

In the diagram we have flag pole AB and C is the point on the ground.

It is given that angle of depression is 30°

and the distance of the point C from the base B is 75 feet

so we have

BC= 75 feet

∠C = 30°

AB= h feet

now in right ΔABC

`tan C = (opposite \ side )/(base) \\tan C=(AB)/(BC)`

now we plug AB= h , ∠C= 30° and BC =75

`tan 30= (h)/(75)`

`75 tan30 = h` ( multiply both sides by 75)

`h= 75 tan 30 =75 (0.5773)\\ h= 43.3 feet\\`

Height of flag pole to the nearest foot is

h= 43 feet