A tree is 15 meters tall. From a point 20 meters away from the base of the tree,

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Question: A tree is 15 meters tall. From a point 20 meters away from the base of the tree, what is the angle of elevation to the top of the tree?

Options:

Correct Answer: 53.13 degrees

Solution:

tan(θ) = height/distance = 15/20; θ = tan⁻¹(15/20) = 36.87 degrees.

A tree is 15 meters tall. From a point 20 meters away from the base of the tree, what is the angle of elevation to the top of the tree?

A tree is 15 meters tall. From a point 20 meters away from the base of the tree, what is the angle of elevation to the top of the tree?

Step 1: Identify the height of the tree, which is 15 meters.
Step 2: Identify the distance from the point to the base of the tree, which is 20 meters.
Step 3: Understand that the angle of elevation (θ) can be found using the tangent function, which relates the height of the tree to the distance from the tree.
Step 4: Use the formula for tangent: tan(θ) = height/distance.
Step 5: Substitute the values into the formula: tan(θ) = 15/20.
Step 6: Simplify the fraction: 15/20 = 0.75.
Step 7: To find the angle θ, use the inverse tangent function: θ = tan⁻¹(0.75).
Step 8: Calculate θ using a calculator: θ ≈ 36.87 degrees.

Trigonometry – The problem involves using the tangent function to find the angle of elevation based on the height of the tree and the distance from the observer.
Right Triangle Properties – Understanding the relationship between the sides of a right triangle and the angles formed, specifically in the context of elevation.