From a point on the ground, the angle of elevation of the top of a hill is 30 degrees. If the distance from the point to the base of the hill is 100 meters, what is the height of the hill?
Practice Questions
1 question
Q1
From a point on the ground, the angle of elevation of the top of a hill is 30 degrees. If the distance from the point to the base of the hill is 100 meters, what is the height of the hill?
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Using tan(30°) = height/100, we have 1/√3 = height/100. Therefore, height = 100/√3 ≈ 57.74 m.
Questions & Step-by-step Solutions
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Q
Q: From a point on the ground, the angle of elevation of the top of a hill is 30 degrees. If the distance from the point to the base of the hill is 100 meters, what is the height of the hill?
Solution: Using tan(30°) = height/100, we have 1/√3 = height/100. Therefore, height = 100/√3 ≈ 57.74 m.
Steps: 9
Step 1: Understand the problem. We have a point on the ground and a hill. We want to find the height of the hill.
Step 2: Identify the angle of elevation. The angle from the point on the ground to the top of the hill is 30 degrees.
Step 3: Know the distance from the point to the base of the hill. This distance is 100 meters.
Step 4: Use the tangent function. The tangent of an angle in a right triangle is the opposite side (height of the hill) divided by the adjacent side (distance to the base).
Step 5: Write the equation using the tangent of 30 degrees. We have tan(30°) = height / 100.
Step 6: Find the value of tan(30°). It is equal to 1/√3.
Step 7: Substitute the value of tan(30°) into the equation: 1/√3 = height / 100.
Step 8: Solve for height. Multiply both sides by 100: height = 100 / √3.
Step 9: Calculate the height. Using a calculator, 100 / √3 is approximately 57.74 meters.
