From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the point is 100 meters away from the base of the hill, 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 45 degrees. If the point is 100 meters away from the base of the hill, 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 45 degrees. If the point is 100 meters away from the base of the hill, what is the height of the hill?
Step 1: Understand the problem. We have a point on the ground and a hill. We need to find the height of the hill.
Step 2: Identify the angle of elevation. The angle of elevation to the top of the hill is given as 45 degrees.
Step 3: Identify the distance from the point to the base of the hill. This distance is 100 meters.
Step 4: Recall the relationship between the height of the hill, the distance from the point to the base, and the angle of elevation. We can use the tangent function: tan(angle) = height / distance.
Step 5: Rearrange the formula to find the height: height = distance * tan(angle).
Step 6: Substitute the values into the formula: height = 100 meters * tan(45 degrees).
Step 7: Calculate tan(45 degrees). The value of tan(45 degrees) is 1.
Step 8: Multiply the distance by the tangent value: height = 100 meters * 1.
Step 9: Conclude that the height of the hill is 100 meters.
