If the angle of elevation of the sun is 30 degrees, how tall is a 10 m pole cast

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Question: If the angle of elevation of the sun is 30 degrees, how tall is a 10 m pole casting a shadow? (2023)

Options:

Correct Answer: 10 m

Exam Year: 2023

Solution:

Height = shadow * tan(angle) = 10 * tan(30) = 10 * (1/√3) ≈ 10 m.

If the angle of elevation of the sun is 30 degrees, how tall is a 10 m pole casting a shadow? (2023)

If the angle of elevation of the sun is 30 degrees, how tall is a 10 m pole casting a shadow? (2023)

Step 1: Understand that the angle of elevation is the angle between the ground and the line from the top of the pole to the sun.
Step 2: Identify the height of the pole, which is 10 meters.
Step 3: Recognize that the shadow of the pole forms a right triangle with the height of the pole and the angle of elevation.
Step 4: Use the tangent function, which relates the angle of elevation to the height of the pole and the length of the shadow. The formula is: Height = Shadow * tan(angle).
Step 5: Substitute the known values into the formula. Here, the angle is 30 degrees, so we need to find tan(30).
Step 6: Calculate tan(30 degrees), which is equal to 1/√3 (approximately 0.577).
Step 7: Substitute tan(30) back into the formula: Height = Shadow * (1/√3).
Step 8: Since the height of the pole is 10 m, we can rearrange the formula to find the shadow: Shadow = Height / tan(30).
Step 9: Calculate the shadow length: Shadow = 10 m / (1/√3) = 10 m * √3 ≈ 17.32 m.
Step 10: Conclude that the height of the pole is 10 m, and the shadow it casts is approximately 17.32 m long.

Trigonometry – The problem involves using the tangent function to relate the height of the pole to the length of its shadow based on the angle of elevation.
Angle of Elevation – Understanding how the angle of elevation affects the height of an object casting a shadow.