A tower is 100 meters high. From a point 80 meters away from the base of the tow

A tower is 100 meters high. From a point 80 meters away from the base of the tower, what is the angle of elevation to the top of the tower?

A tower is 100 meters high. From a point 80 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 100 meters.
Step 2: Identify the distance from the point to the base of the tower, which is 80 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) = 100/80.
Step 5: Simplify the fraction: 100/80 = 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 problem involves using the tangent function to find the angle of elevation based on the height of the tower and the distance from the observer.
Right Triangle Properties – Understanding the relationship between the sides of a right triangle and the angles formed, specifically in the context of elevation.