A building is 40 meters tall. From a point 30 meters away from the base of the b

A building is 40 meters tall. From a point 30 meters away from the base of the building, what is the angle of elevation to the top of the building?

A building is 40 meters tall. From a point 30 meters away from the base of the building, what is the angle of elevation to the top of the building?

Step 1: Identify the height of the building, which is 40 meters.
Step 2: Identify the distance from the point to the base of the building, which is 30 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) = 40/30.
Step 5: Simplify the fraction: 40/30 = 4/3.
Step 6: To find the angle θ, use the inverse tangent function: θ = tan⁻¹(4/3).
Step 7: Calculate θ 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.