A man is standing on the ground and looking at the top of a 15 m high pole. If h
Practice Questions
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
45 degrees
60 degrees
30 degrees
Questions & Step-by-Step Solutions
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?
Correct Answer: 36.87 degrees
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.
Trigonometry – The question tests the understanding of the tangent function in right triangles, specifically how to calculate the angle of elevation using the ratio of the opposite side (height of the pole) to the adjacent side (distance from the pole).
Inverse Trigonometric Functions – It assesses the ability to apply the inverse tangent function to find the angle from the tangent ratio.
