A man is standing 50 meters away from a vertical pole. If he looks up at an angle of elevation of 60 degrees to the top of the pole, what is the height of the pole?
Practice Questions
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Q1
A man is standing 50 meters away from a vertical pole. If he looks up at an angle of elevation of 60 degrees to the top of the pole, what is the height of the pole?
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Using tan(60°) = height/50, we have √3 = height/50. Therefore, height = 50√3 ≈ 86.6 m.
Questions & Step-by-step Solutions
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Q
Q: A man is standing 50 meters away from a vertical pole. If he looks up at an angle of elevation of 60 degrees to the top of the pole, what is the height of the pole?
Solution: Using tan(60°) = height/50, we have √3 = height/50. Therefore, height = 50√3 ≈ 86.6 m.
Steps: 8
Step 1: Understand the problem. A man is standing 50 meters away from a vertical pole and looking up at an angle of 60 degrees.
Step 2: Visualize the situation. Imagine a right triangle where the man is at one point, the top of the pole is the second point, and the base of the pole is the third point.
Step 3: Identify the sides of the triangle. The distance from the man to the pole is the base (50 meters), the height of the pole is the opposite side, and the angle of elevation is 60 degrees.
Step 4: Use the tangent function. The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. Here, tan(60°) = height / 50.
Step 5: Find the value of tan(60°). We know that tan(60°) = √3.
Step 6: Set up the equation. Replace tan(60°) in the equation: √3 = height / 50.
Step 7: Solve for height. Multiply both sides by 50: height = 50 * √3.
Step 8: Calculate the height. Using a calculator, find that 50 * √3 is approximately 86.6 meters.
