From a point on the ground, the angle of elevation to the top of a hill is 37 degrees. If the distance from the point to the base of the hill is 50 meters, what is the height of the hill?
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From a point on the ground, the angle of elevation to the top of a hill is 37 degrees. If the distance from the point to the base of the hill is 50 meters, what is the height of the hill?
Q: From a point on the ground, the angle of elevation to the top of a hill is 37 degrees. If the distance from the point to the base of the hill is 50 meters, what is the height of the hill?
Step 1: Understand the problem. We need to find the height of a hill using the angle of elevation and the distance from the point to the base of the hill.
Step 2: Identify the given information. The angle of elevation is 37 degrees, and the distance from the point to the base of the hill is 50 meters.
Step 3: Recall the relationship between the angle of elevation, the height of the hill, and the distance to the base. We can use the tangent function: tan(angle) = height / distance.
Step 4: Rearrange the formula to find the height: height = distance * tan(angle).
Step 5: Plug in the values: height = 50 * tan(37 degrees).
Step 6: Calculate tan(37 degrees) using a calculator or a trigonometric table. It is approximately 0.7536.
Step 7: Multiply the distance by the tangent value: height = 50 * 0.7536.
Step 8: Perform the multiplication: height ≈ 37.68 meters.
Step 9: Round the answer if necessary. The height of the hill is approximately 30 meters.
