A man is standing on the ground and looking at the top of a 15 m high pole. If he is 20 m away from the base of the pole, what is the angle of elevation?
Practice Questions
1 question
Q1
A man is standing on the ground and looking at the top of a 15 m high pole. If he is 20 m away from the base of the pole, what is the angle of elevation?
36.87 degrees
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30 degrees
Using tan(θ) = height/distance, we have tan(θ) = 15/20. Therefore, θ = tan⁻¹(0.75) which is approximately 36.87 degrees.
Questions & Step-by-step Solutions
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Q
Q: A man is standing on the ground and looking at the top of a 15 m high pole. If he is 20 m away from the base of the pole, what is the angle of elevation?
Solution: Using tan(θ) = height/distance, we have tan(θ) = 15/20. Therefore, θ = tan⁻¹(0.75) which is approximately 36.87 degrees.
Steps: 8
Step 1: Identify the height of the pole, which is 15 meters.
Step 2: Identify the distance from the man to the base of the pole, which is 20 meters.
Step 3: Understand that the angle of elevation is the angle formed between the line of sight from the man to the top of the pole and the horizontal line from the man to the base of the pole.
Step 4: Use the tangent function, which relates the angle of elevation (θ) to the opposite side (height of the pole) and the adjacent side (distance from the pole). The formula is tan(θ) = height/distance.
Step 5: Substitute the values into the formula: tan(θ) = 15/20.
Step 6: Simplify the fraction: 15/20 = 0.75.
Step 7: To find the angle θ, use the inverse tangent function: θ = tan⁻¹(0.75).
Step 8: Calculate θ using a calculator or trigonometric table, which gives approximately 36.87 degrees.
