A 12-meter tall pole casts a shadow of 6 meters. What is the angle of elevation

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Question: A 12-meter tall pole casts a shadow of 6 meters. What is the angle of elevation of the sun?

Options:

Correct Answer: 60 degrees

Solution:

Using tan(θ) = height / shadow length, we have θ = tan⁻¹(12/6) = tan⁻¹(2) which corresponds to approximately 60 degrees.

A 12-meter tall pole casts a shadow of 6 meters. What is the angle of elevation of the sun?

A 12-meter tall pole casts a shadow of 6 meters. What is the angle of elevation of the sun?

Step 1: Identify the height of the pole, which is 12 meters.
Step 2: Identify the length of the shadow, which is 6 meters.
Step 3: Use the formula for the tangent of the angle of elevation: tan(θ) = height / shadow length.
Step 4: Substitute the values into the formula: tan(θ) = 12 / 6.
Step 5: Simplify the fraction: tan(θ) = 2.
Step 6: To find the angle θ, use the inverse tangent function: θ = tan⁻¹(2).
Step 7: Calculate the angle using a calculator or trigonometric table: θ is approximately 60 degrees.

Trigonometry – The problem involves using the tangent function to relate the height of the pole and the length of the shadow to find the angle of elevation.
Inverse Trigonometric Functions – The solution requires the use of the inverse tangent function (tan⁻¹) to determine the angle from the ratio of the opposite side (height) to the adjacent side (shadow length).