A tree is 10 meters tall. From a point 20 meters away from the base of the tree,

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Question: A tree is 10 meters tall. From a point 20 meters away from the base of the tree, the angle of elevation to the top of the tree is what?

Options:

Correct Answer: 36.87 degrees

Solution:

tan(θ) = height/distance = 10/20 => θ = tan⁻¹(0.5) = 26.57 degrees

A tree is 10 meters tall. From a point 20 meters away from the base of the tree, the angle of elevation to the top of the tree is what?

A tree is 10 meters tall. From a point 20 meters away from the base of the tree, the angle of elevation to the top of the tree is what?

Step 1: Identify the height of the tree, which is 10 meters.
Step 2: Identify the distance from the point to the base of the tree, which is 20 meters.
Step 3: Understand that we need to find the angle of elevation (θ) to the top of the tree.
Step 4: Use the tangent function, which relates the angle to the opposite side (height of the tree) and the adjacent side (distance from the tree).
Step 5: Set up the equation: tan(θ) = height/distance = 10/20.
Step 6: Simplify the fraction: 10/20 = 0.5.
Step 7: Use the inverse tangent function to find θ: θ = tan⁻¹(0.5).
Step 8: Calculate θ using a calculator or trigonometric table to find that θ ≈ 26.57 degrees.

Trigonometry – The question tests the understanding of the tangent function in right triangles, specifically how to calculate the angle of elevation using the ratio of the opposite side (height of the tree) to the adjacent side (distance from the tree).
Angle of Elevation – The concept of angle of elevation is crucial, as it refers to the angle formed by the horizontal line from the observer's eye to the line of sight to the top of the object.