If the angle of elevation of the sun is 30 degrees, how tall is a 10-meter pole

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Question: If the angle of elevation of the sun is 30 degrees, how tall is a 10-meter pole casting a shadow of 10√3 meters? (2023)

Options:

Correct Answer: 10 m

Exam Year: 2023

Solution:

Height = Shadow * tan(30) = 10√3 * (1/√3) = 10 m.

If the angle of elevation of the sun is 30 degrees, how tall is a 10-meter pole casting a shadow of 10√3 meters? (2023)

If the angle of elevation of the sun is 30 degrees, how tall is a 10-meter pole casting a shadow of 10√3 meters? (2023)

Step 1: Understand that the angle of elevation of the sun is 30 degrees.
Step 2: Know that the height of the pole and the length of the shadow form a right triangle with the angle of elevation.
Step 3: Use the tangent function, which relates the angle to the opposite side (height of the pole) and the adjacent side (length of the shadow).
Step 4: The formula for tangent is tan(angle) = opposite/adjacent. Here, opposite is the height of the pole and adjacent is the length of the shadow.
Step 5: For an angle of 30 degrees, tan(30) = 1/√3.
Step 6: Set up the equation: Height = Shadow * tan(30).
Step 7: Substitute the values: Height = 10√3 * (1/√3).
Step 8: Simplify the equation: Height = 10 meters.

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