From a point 60 meters away from the base of a hill, the angle of elevation to the top of the hill is 30 degrees. What is the height of the hill?

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Q: From a point 60 meters away from the base of a hill, the angle of elevation to the top of the hill is 30 degrees. What is the height of the hill?

Solution: Height = distance * tan(angle) = 60 * (1/√3) = 60 / 1.732 = 34.64 meters.

Steps: 8

Step 1: Understand the problem. You are looking for the height of a hill from a point 60 meters away.
Step 2: Identify the angle of elevation. The angle given is 30 degrees.
Step 3: Recall the relationship between the height of the hill, the distance from the hill, and the angle of elevation. This can be calculated using the tangent function: tan(angle) = height / distance.
Step 4: Rearrange the formula to find the height: height = distance * tan(angle).
Step 5: Substitute the values into the formula. Here, distance = 60 meters and angle = 30 degrees.
Step 6: Calculate tan(30 degrees). The value of tan(30 degrees) is 1/√3 or approximately 0.577.
Step 7: Multiply the distance by the tangent value: height = 60 * (1/√3).
Step 8: Calculate the height: height = 60 / 1.732, which is approximately 34.64 meters.