A person is standing 50 meters away from a vertical pole. If the angle of elevation of the top of the pole is 60 degrees, what is the height of the pole?
Practice Questions
1 question
Q1
A person is standing 50 meters away from a vertical pole. If the angle of elevation of the top of the pole is 60 degrees, what is the height of the pole?
25 m
30 m
35 m
40 m
Using tan(60°) = height/50, we have √3 = height/50. Therefore, height = 50√3 ≈ 86.6 m.
Questions & Step-by-step Solutions
1 item
Q
Q: A person is standing 50 meters away from a vertical pole. If the angle of elevation of the top of the pole is 60 degrees, 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: 10
Step 1: Understand the problem. You have a pole and a person standing 50 meters away from it.
Step 2: The angle of elevation to the top of the pole is given as 60 degrees.
Step 3: Recall the tangent function in a right triangle: tan(angle) = opposite side / adjacent side.
Step 4: In this case, the opposite side is the height of the pole, and the adjacent side is the distance from the person to the pole (50 meters).
Step 5: Write the equation using the tangent of the angle: tan(60°) = height / 50.
Step 6: Find the value of tan(60°). It is equal to √3.
Step 7: Substitute tan(60°) into the equation: √3 = height / 50.
Step 8: To find the height, multiply both sides of the equation by 50: height = 50 * √3.
