A person is standing 50 meters away from a vertical pole. If the angle of elevat
Practice Questions
Q1
A person is standing 50 meters away from a vertical pole. If the angle of elevation to the top of the pole is 60 degrees, what is the height of the pole?
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Questions & Step-by-Step Solutions
A person is standing 50 meters away from a vertical pole. If the angle of elevation to the top of the pole is 60 degrees, what is the height of the pole?
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: Visualize a right triangle formed by the pole, the ground, and the line of sight from the person to the top of the pole.
Step 4: In this triangle, the distance from the person to the base of the pole is the adjacent side (50 meters), and the height of the pole is the opposite side.
Step 5: Use the tangent function, which relates the angle to the opposite and adjacent sides: tan(angle) = opposite/adjacent.
Step 6: Substitute the known values into the formula: tan(60°) = height/50.
Step 7: We know that tan(60°) is equal to √3. So, we can write: √3 = height/50.
Step 8: To find the height, multiply both sides of the equation by 50: height = 50 * √3.
Step 9: Calculate the height: height ≈ 50 * 1.732 (since √3 is approximately 1.732).
Step 10: Therefore, height ≈ 86.6 meters.
Trigonometry – The problem tests the understanding of the tangent function in right triangles, specifically how to relate angles and side lengths.
Angle of Elevation – The question involves calculating the height of an object using the angle of elevation from a certain distance.
