A building is 50 meters tall. From a point 40 meters away from the base of the b

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

A building is 50 meters tall. From a point 40 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 50 meters.
Step 2: Identify the distance from the point to the base of the building, 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 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 ratio.