A 15-meter tall tree casts a shadow of 10 meters. What is the angle of elevation

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Question: A 15-meter tall tree casts a shadow of 10 meters. What is the angle of elevation of the sun? (2019)

Options:

Correct Answer: 60 degrees

Exam Year: 2019

Solution:

tan(θ) = height/shadow = 15/10 = 1.5, θ = tan⁻¹(1.5) ≈ 56.31 degrees, which is closest to 60 degrees.

A 15-meter tall tree casts a shadow of 10 meters. What is the angle of elevation of the sun? (2019)

A 15-meter tall tree casts a shadow of 10 meters. What is the angle of elevation of the sun? (2019)

Correct Answer: 60 degrees

Step 1: Identify the height of the tree, which is 15 meters.
Step 2: Identify the length of the shadow, which is 10 meters.
Step 3: Use the formula for tangent, which is tan(θ) = height/shadow.
Step 4: Substitute the values into the formula: tan(θ) = 15/10.
Step 5: Calculate the value: 15 divided by 10 equals 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 56.31 degrees.
Step 8: Round the angle to the nearest whole number, which is closest to 60 degrees.

Trigonometry – The problem involves using the tangent function to find the angle of elevation based on the ratio of the height of the tree to the length of its shadow.
Angle of Elevation – Understanding the concept of angle of elevation, which is the angle formed by the line of sight from the observer to the top of an object above the horizontal.