A 12-meter tall building casts a shadow of 8 meters. What is the angle of elevat

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Question: A 12-meter tall building casts a shadow of 8 meters. What is the angle of elevation of the sun?

Options:

Correct Answer: 36.87 degrees

Solution:

Using tan(θ) = height/shadow = 12/8 = 1.5, θ = tan⁻¹(1.5) ≈ 36.87 degrees.

A 12-meter tall building casts a shadow of 8 meters. What is the angle of elevation of the sun?

A 12-meter tall building casts a shadow of 8 meters. What is the angle of elevation of the sun?

Step 1: Identify the height of the building, which is 12 meters.
Step 2: Identify the length of the shadow, which is 8 meters.
Step 3: Use the tangent function, which relates the angle of elevation (θ) to the height and shadow length. The formula is tan(θ) = height / shadow.
Step 4: Substitute the values into the formula: tan(θ) = 12 / 8.
Step 5: Simplify the fraction: 12 / 8 = 1.5.
Step 6: Now, find the angle θ by using the inverse tangent function: θ = tan⁻¹(1.5).
Step 7: Use a calculator to find tan⁻¹(1.5), which is approximately 36.87 degrees.

Trigonometry – The problem involves using the tangent function to relate the height of the building and the length of the shadow to find the angle of elevation.
Angle of Elevation – Understanding the concept of angle of elevation as the angle formed by the line of sight from the observer to the top of the object.