A person is standing at a distance of 20 m from a vertical pole. If the angle of elevation to the top of the pole is 45 degrees, what is the height of the pole?
Practice Questions
1 question
Q1
A person is standing at a distance of 20 m from a vertical pole. If the angle of elevation to the top of the pole is 45 degrees, what is the height of the pole?
20 m
10 m
30 m
15 m
Using tan(45°) = height/distance, we have height = distance * tan(45°) = 20 * 1 = 20 m.
Questions & Step-by-step Solutions
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Q
Q: A person is standing at a distance of 20 m from a vertical pole. If the angle of elevation to the top of the pole is 45 degrees, what is the height of the pole?
Solution: Using tan(45°) = height/distance, we have height = distance * tan(45°) = 20 * 1 = 20 m.
Steps: 8
Step 1: Understand the problem. You have a person standing 20 meters away from a vertical pole.
Step 2: Know that the angle of elevation to the top of the pole is 45 degrees.
Step 3: Recall the tangent function in trigonometry, which relates the angle to the opposite side (height of the pole) and the adjacent side (distance from the pole).
Step 4: Write the formula: tan(angle) = height / distance.
Step 5: Substitute the known values into the formula: tan(45°) = height / 20 m.
Step 6: Know that tan(45°) equals 1. So, the equation becomes: 1 = height / 20 m.
Step 7: Solve for height by multiplying both sides by 20 m: height = 20 m * 1.
Step 8: Conclude that the height of the pole is 20 meters.
