The angles of elevation of the top of a tower from two
points at a distance of 9 meters and 16 meters from the
base of the tower and in the same straight line with it, are
55° and 35° respectively. The height of the tower is
.
Answers
Answer:
Answer:
Height of Tower = 12 metres
Explanation:
The angles of Elevation of the top of a tower from two points at a distance of 9 metres and 16 metres from the base of the tower in the same straight line are given as 55° and 35°
Refer to the attached image for figure
Now, Let height of tower be h
and since,
tan θ = opposite side / adjacent side
therefore,
→ tan 35° = h / 16 ___equation (1)
and,
→ tan 55° = h / 9
→ tan ( 90° - 35° ) = h / 9
Since, tan (90 - θ) = cot θ, therefore
→ cot 35° = h / 9
→ 1/tan 35° = h / 9
→ tan 35° = 9 / h
using equation (1)
→ h / 16 = 9 / h
→ h² = 16 × 9
→ h² = 144
→ h = 12 metres
Therefore,
Height of Tower is 12 metres.
Answer:
Answer:
Height of Tower = 12 metres
Explanation:
The angles of Elevation of the top of a tower from two points at a distance of 9 metres and 16 metres from the base of the tower in the same straight line are given as 55° and 35°
Refer to the attached image for figure
Now, Let height of tower be h
and since,
tan θ = opposite side / adjacent side
therefore,
→ tan 35° = h / 16 ___equation (1)
and,
→ tan 55° = h / 9
→ tan ( 90° - 35° ) = h / 9
Since, tan (90 - θ) = cot θ, therefore
→ cot 35° = h / 9
→ 1/tan 35° = h / 9
→ tan 35° = 9 / h
using equation (1)
→ h / 16 = 9 / h
→ h² = 16 × 9
→ h² = 144
→ h = 12 metres
Therefore,
Height of Tower is 12 metres.