A tower is 50 meters high. From a point 40 meters away from the base of the towe

A tower is 50 meters high. From a point 40 meters away from the base of the tower, what is the angle of elevation to the top of the tower?

A tower is 50 meters high. From a point 40 meters away from the base of the tower, what is the angle of elevation to the top of the tower?

Correct Answer: 51.34 degrees

Step 1: Identify the height of the tower, which is 50 meters.
Step 2: Identify the distance from the point to the base of the tower, which is 40 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) = 50 / 40.
Step 5: Simplify the fraction: 50 / 40 = 1.25.
Step 6: To find the angle θ, use the inverse tangent function: θ = tan⁻¹(1.25).
Step 7: Calculate θ using a calculator: θ ≈ 51.34 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 tower) to the adjacent side (distance from the tower).
Inverse Trigonometric Functions – It assesses the ability to apply the inverse tangent function (tan⁻¹) to find the angle from the tangent ratio.