To measure the height of a cloud, you place a bright searchlight directly below the cloud and shine the beam straight up. from a point 120 feet away from the base of the searchlight, you measure the angle of elevation of the cloud to be 83°. how high is the cloud? round your answer to the nearest foot.

The cloud is at height 977 feet to the nearest foot

Step-by-step 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

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step-by-step explanation: