A tightrope walker is moving along a tightrope at 3 ft/sec at an altitude of 100 feet. The walker is tracked by a searchlight on the ground. Find the change in the angle of elevation of the searchlight when the walker is 200 feet horizontally from the light and walking away from the light

Change in the angle of elevation = 63.4°

The original position of the tightrope Walker is vertical

That is, the initial angle of elevation, θ = 90 degrees

Horizontal distance of the Walker = 200 feet

The altitude of the Walker = 100 feet

The final angle of elevation of the tightrope Walker is calculated as follows

Change in the angle of elevation = Final angle of elevation - Initial angle of elevation

Change in the angle of elevation = 90 - 26.6

Change in the angle of elevation = 63.4°

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The change in the angle of elevation is approximately 63.435°

Step-by-step explanation:

The given parameters are;

The speed of the tightrope walker = 3 ft./sec

The altitude at which the tightrope walker is moving = 100 ft.

The horizontal distance of the tightrope walker from the searchlight = 200 feet

The final angle of elevation, θ, is given by the trigonometric ratio as follows;

Whereby the tightrope walker was initially vertically overhead the search light, the initial angle of elevation = 90°

The change in the angle of elevation = The initial angle of elevation - The final angle of elevation

Substituting the values gives

The change in the angle of elevation = 90° - 26.565 ≈ 63.435°

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step-by-step explanation: