Question

A surveyor observes that point A is located on level ground 25 feet from a flag pole. The base of the flagpole represents point B. Approximate the height of the flagpole to the nearest tenth of a foot when the angle between the ground and the top of the flagpole is:______.(a) 30° (b) 38° (c) 45°

Answer 1

Explanation:

The set up will give a right angled triangle

Given

Distance of point A from the flagpole = 25feet

If angle of elevation is 30°

Required

Height of flagpole (opposite)

Using TOA

tan theta = opp/adj

tan30° = opp/25

opp = 25tan30°

opp = 14.4feet

Hence the height of flagpole when the angle of elevation is 30° is 14.4feet

If angle of elevation is 38°

Required

Height of flagpole (opposite)

Using TOA

tan theta = opp/adj

tan38° = opp/25

opp = 25tan38°

opp = 19.53feet

Hence the height of flagpole when the angle of elevation is 38° is 19.5feet

If angle of elevation is 45°

Required

Height of flagpole (opposite)

Using TOA

tan theta = opp/adj

tan45° = opp/25

opp = 25tan45°

opp = 25feet

Hence the height of flagpole when the angle of elevation is 45° is 25feet