A building is 80 meters tall. From a point 60 meters away from the base of the b

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Question: A building is 80 meters tall. From a point 60 meters away from the base of the building, the angle of elevation to the top of the building is what?

Options:

45 degrees
60 degrees
30 degrees
75 degrees

Correct Answer: 60 degrees

Solution:

Using tan(θ) = height/distance, tan(θ) = 80/60, θ = tan⁻¹(4/3) ≈ 53.13 degrees.

A building is 80 meters tall. From a point 60 meters away from the base of the b

Practice Questions

A building is 80 meters tall. From a point 60 meters away from the base of the building, the angle of elevation to the top of the building is what?

45 degrees
60 degrees
30 degrees
75 degrees

Questions & Step-by-Step Solutions

A building is 80 meters tall. From a point 60 meters away from the base of the building, the angle of elevation to the top of the building is what?

Correct Answer: 53.13 degrees

Step 1: Identify the height of the building, which is 80 meters.
Step 2: Identify the distance from the point to the base of the building, which is 60 meters.
Step 3: Use the formula for the tangent of the angle of elevation: tan(θ) = height / distance.
Step 4: Substitute the values into the formula: tan(θ) = 80 / 60.
Step 5: Simplify the fraction: 80 / 60 = 4 / 3.
Step 6: Use the inverse tangent function to find the angle: θ = tan⁻¹(4/3).
Step 7: Calculate the angle using a calculator: θ ≈ 53.13 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 building) to the adjacent side (distance from the building).
Inverse Trigonometric Functions – The solution requires the use of the inverse tangent function (tan⁻¹) to find the angle from the tangent ratio.

A building is 80 meters tall. From a point 60 meters away from the base of the b

What’s inside this PDF?

A building is 80 meters tall. From a point 60 meters away from the base of the b

Practice Questions

Questions & Step-by-Step Solutions

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