A person is standing 40 meters away from a tower. If the angle of elevation to t

A person is standing 40 meters away from a tower. If the angle of elevation to the top of the tower is 45 degrees, what is the height of the tower?

A person is standing 40 meters away from a tower. If the angle of elevation to the top of the tower is 45 degrees, what is the height of the tower?

Correct Answer: 40 meters

Step 1: Understand the problem. You have a person standing 40 meters away from a tower and looking up at the top of the tower.
Step 2: Identify the angle of elevation. The angle at which the person looks up to the top of the tower is 45 degrees.
Step 3: Recall the relationship between the angle of elevation, the height of the tower, and the distance from the tower. This can be calculated using the tangent function.
Step 4: Use the formula for height: Height = distance * tan(angle). Here, the distance is 40 meters and the angle is 45 degrees.
Step 5: Calculate tan(45 degrees). The tangent of 45 degrees is 1.
Step 6: Substitute the values into the formula: Height = 40 meters * 1.
Step 7: Calculate the height. The height of the tower is 40 meters.

Trigonometry – The problem involves using the tangent function to relate the height of the tower to the distance from the tower and the angle of elevation.
Angle of Elevation – Understanding how the angle of elevation relates to the height and distance in a right triangle.