From a point on the ground, the angle of elevation to the top of a hill is 30 degrees. If the point is 100 meters away from the base of the hill, what is the height of the hill?

Practice Questions

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50 meters
100 meters
100√3 meters
50√3 meters

Questions & Step-by-step Solutions

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Q: From a point on the ground, the angle of elevation to the top of a hill is 30 degrees. If the point is 100 meters away from the base of the hill, what is the height of the hill?

Solution: Height = distance * tan(angle) = 100 * (1/√3) = 100/√3 = 50√3 meters.

Steps: 9

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 30 degrees.
Step 3: Identify the distance from the point to the base of the hill. This distance is 100 meters.
Step 4: Use the tangent function. The height of the hill can be found using the formula: Height = distance * tan(angle).
Step 5: Calculate the tangent of the angle. For 30 degrees, tan(30 degrees) = 1/√3.
Step 6: Substitute the values into the formula. Height = 100 * (1/√3).
Step 7: Simplify the calculation. This gives us Height = 100/√3.
Step 8: To express the height in a simpler form, multiply the numerator and denominator by √3. This gives us Height = 100√3/3.
Step 9: Calculate the final height. The height of the hill is approximately 50√3 meters.

From a point on the ground, the angle of elevation to the top of a hill is 30 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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Questions & Step-by-step Solutions

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