From a point on the ground, the angle of elevation to the top of a hill is 30 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 30 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 30 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 given the angle of elevation and the distance from the point to the base of the hill.
Step 2: Identify the angle of elevation. The angle given is 30 degrees.
Step 3: Identify the distance from the point to the base of the hill. This distance is 50 meters.
Step 4: Use the tangent function. The formula to find the height (h) using the tangent of the angle is: h = distance * tan(angle).
Step 5: Substitute the values into the formula. Here, h = 50 * tan(30 degrees).
Step 6: Calculate tan(30 degrees). The value of tan(30 degrees) is 1/√3 (approximately 0.577).
Step 7: Multiply the distance by the tangent value. So, h = 50 * (1/√3).
Step 8: Calculate the height. This gives us h ≈ 50 * 0.577 ≈ 28.87 meters.
