Problem

22. The angle of elevation to the top of a building is found to be $30^{\circ}$ from the ground at a distance of 650 feet from the base of the building. Using this information, which expression below could be used to calculate the height of the building?

Answer

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Answer

Final Answer: The expression to calculate the height of the building is \(\boxed{650 \cdot \tan(30^{\circ})}\). The height of the building is approximately \(\boxed{375.28}\) feet.

Steps

Step 1 :The problem involves trigonometry. Specifically, it involves the tangent of the angle of elevation, which is the ratio of the opposite side (the height of the building) to the adjacent side (the distance from the base of the building). Therefore, the height of the building can be calculated as the tangent of the angle of elevation times the distance from the base of the building.

Step 2 :Given: angle = 30 degrees, distance = 650 feet

Step 3 :Convert the angle to radians: angle_rad = 0.5235987755982988

Step 4 :Calculate the height of the building: height = 650 * tan(angle_rad) = 375.27767497325675 feet

Step 5 :Final Answer: The expression to calculate the height of the building is \(\boxed{650 \cdot \tan(30^{\circ})}\). The height of the building is approximately \(\boxed{375.28}\) feet.

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