A building is 100 m tall. From a point 80 m away from the base of the building,

A building is 100 m tall. From a point 80 m away from the base of the building, the angle of elevation to the top of the building is what?

A building is 100 m tall. From a point 80 m away from the base of the building, the angle of elevation to the top of the building is what?

Correct Answer: 60 degrees

Step 1: Identify the height of the building, which is 100 meters.
Step 2: Identify the distance from the point to the base of the building, which is 80 meters.
Step 3: Use the tangent function, which relates the angle of elevation (θ) to the height and distance: tan(θ) = height/distance.
Step 4: Substitute the values into the formula: tan(θ) = 100/80.
Step 5: Calculate 100 divided by 80, which equals 1.25.
Step 6: Now, find the angle θ by using the inverse tangent function: θ = tan⁻¹(1.25).
Step 7: Use a calculator to find tan⁻¹(1.25), which is approximately 60 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 question requires the use of the inverse tangent function (tan⁻¹) to find the angle from the tangent value.