Question

please fast answer. to find the height of the pole, a surveyor uses a theodolite. the theodolite is 4 ft tall. the surveyor stands 140 feet away from the base of the pole . then she measures the angle of elevation to the top of the pole to be 44. what is the height of the pole? round to the nearest foot.​

Answer 1

C. 139 ft

Explanation:

Height of the pole = x + 4 ft

First, find x using trigonometric function.

Reference angle = 44°

Opposite side length = x

Adjacent side length = 140 ft

Apply TOA, which is:

Tan 44 = opp/adj

Tan 44 = x/140

Multiply both sides by 140

140 × Tan 44 = x

135.196428 = x

x ≈ 135 ft

✔️Height of the pole = x + 4 ft = 135 + 4 = 139 ft