A 40-meter tall tree casts a shadow of 20 meters. What is the angle of elevation

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Question: A 40-meter tall tree casts a shadow of 20 meters. What is the angle of elevation of the sun?

Options:

Correct Answer: 60 degrees

Solution:

Using tan(θ) = height/shadow length, θ = tan^(-1)(40/20) = tan^(-1)(2) = 60 degrees.

A 40-meter tall tree casts a shadow of 20 meters. What is the angle of elevation of the sun?

A 40-meter tall tree casts a shadow of 20 meters. What is the angle of elevation of the sun?

Step 1: Identify the height of the tree, which is 40 meters.
Step 2: Identify the length of the shadow, which is 20 meters.
Step 3: Use the formula for the tangent of the angle of elevation, which is tan(θ) = height / shadow length.
Step 4: Substitute the values into the formula: tan(θ) = 40 / 20.
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: θ = 60 degrees.

Trigonometry – The problem tests the understanding of the tangent function in right triangles, specifically how to relate the height of an object and the length of its shadow to find the angle of elevation.
Inverse Trigonometric Functions – The question requires the use of the inverse tangent function (tan^(-1)) to find the angle from the ratio of the opposite side (height) to the adjacent side (shadow length).