Answer:
The cloud is at height 977 feet to the nearest foot
Explanation:
* Lets explain how to solve this problem
- You place a bright searchlight directly below the cloud and shine the
beam straight up to measure the height of the cloud
- You measure the angle of elevation of the cloud from a point 120 feet
away from the base of the searchlight
- The measure of the angle of elevation is 83°
- Lets consider the the height of the cloud and the distance between
the base of the searchlight and the point of the angle of elevation
(120 feet) are the legs of a right triangle
∴ We have a right triangle the height of the cloud is the opposite
side to the angle of elevation (83°)
∵ The distance between the base of the searchlight and the point
of the angle of elevation (120 feet) is the adjacent side of the
angle of elevation (83°)
- By using the trigonometry function tan Ф
∵ Ф is the angle of elevation
∴ Ф = 83°
∵ tan Ф = opposite /adjacent
∵ The side opposite is h (height of the cloud)
∵ The adjacent side to Ф is 120 feet
∴ tan 83° = h/120 ⇒ by using cross multiplication
∴ h = 120 × tan 83° = 977.322 ≅ 977 feet
* The cloud is at height 977 feet