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A mine shaft with a circular entrance has been carved into the side of a mountain. From a distance of 350
feet from the base of the mountain, the angle of elevation to the bottom of the circular opening is .
The angle of elevation to the top of the opening is . Determine the diameter of the circular entrance.
The diameter of the mine shaft entrance is
(Do not round until the final answer. Then round to two decimal places as needed.)

Ask by Gordon Summers. in the United States
Mar 28,2025

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The diameter of the mine shaft entrance is approximately 25.09 feet.

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Beyond the Answer

To determine the diameter of the circular entrance, we can use trigonometry. Given the angle of elevation to the bottom of the circular opening is and to the top is , we can compute the heights using tangent functions.
Let be the height to the bottom of the entrance and be the height to the top of the entrance. The distance from the base of the mountain is feet.
Calculate :
Using a calculator,
Calculate :
Using a calculator,
Determine the height of the entrance:
The height of the circular entrance is:
Assuming the entrance is circular, the diameter is equal to the height of the entrance:
Therefore, the diameter of the mine shaft entrance is approximately feet, rounded to two decimal places as needed.

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