A tower is 50 meters high. From a point 30 meters away from the base of the towe

A tower is 50 meters high. From a point 30 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 30 meters away from the base of the tower, what is the angle of elevation to the top of the tower?

Correct Answer: 60 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 30 meters.
Step 3: Understand that the angle of elevation (θ) is the angle formed between the line of sight to the top of the tower and the horizontal line from the point to the base of the tower.
Step 4: Use the tangent function, which relates the angle of elevation to the opposite side (height of the tower) and the adjacent side (distance from the tower). The formula is tan(θ) = height / distance.
Step 5: Substitute the values into the formula: tan(θ) = 50 / 30.
Step 6: Simplify the fraction: 50 / 30 = 5 / 3.
Step 7: To find the angle θ, use the inverse tangent function: θ = tan^(-1)(5/3).
Step 8: Calculate θ using a calculator to find that θ is approximately 60 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.