5 The angle of elevation of the top of a tower from the foot of a building is 30° and the angle of elevation of the top of the building from the foot of the tower is 60°. What is the ratio of heights of towers and building.
Answers
Let the height of the tower be AB and the height of the building be CD.
The angle of elevation of the top of building D from the foot of tower B is 30° and the angle of elevation of the top of tower A from the foot of building C is 60°.
Distance between the foot of the tower and the building is BC.
Trigonometric ratio involving sides AB, CD, BC and angles ∠B and ∠C is tan θ.
In ΔABC,
tan 60° = AB/BC
√3 = 50/BC
BC = 50/√3 ....(i)
In ΔBCD,
tan 30° = CD / BC
1/√3 = CD / BC
1/√3 = CD / 50/√3 [from (i)]
CD = 1/√3 × 50/√3
CD = 50/3
Height of the building CD = 50/3 m.
Answer:
Summary: If the angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60° and if the tower is 50 m high, then the height of the building is 50/3 m.