Question

From a point 5 ft above the ground and 20 ft from the base of a building, a surveyor uses a transit to sight an angle of 38° degrees to the top of the building.

Find the height of the building.

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Answer 1

To find the height of the building, we can use the tangent function to calculate the height based on the angle of elevation and the distance from the base of the building. Using the given values, we find that the height of the building is approximately 13.96 feet.

Step-by-step explanation:

To find the height of the building, we can use the concept of trigonometry. Since we know the angle of elevation and the distance from the base of the building, we can use the tangent function to calculate the height.

First, we convert the angle to radians by multiplying it by π/180:

38° × π/180 = 0.6632 radians

Next, we can use the tangent function to find the height:

tan(0.6632) = height / 20 ft

height = tan(0.6632) × 20 ft

Using a calculator, we can find that:

height ≈ 13.96 ft

So the height of the building is approximately 13.96 feet.