An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from his/her eyes has measure 45 degrees. What is the height of the tower?

• A. 28.5 m
• B. 30 m
• C. 27 m
• D. 1.5 m

To find the height of the tower, we can use trigonometry. The observer's height is 1.5 m, and they are 28.5 m away from the tower. The angle of elevation to the top of the tower is 45 degrees.

Step-by-Step Calculation

We can visualize this situation as a right triangle where:

• The distance from the observer to the tower is the base (28.5 m).
• The height of the tower above the observer's eye level is the opposite side.
• The angle of elevation is 45 degrees.

Using Tangent Function

The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. Thus, we have:

tan(45°) = opposite / adjacent

Since tan(45°) equals 1, we can set up the equation:

1 = height above eye level / 28.5 m

This means:

height above eye level = 28.5 m

Calculating Total Height of the Tower

Now, to find the total height of the tower, we add the observer's height:

Total height = height above eye level + observer's height

Total height = 28.5 m + 1.5 m = 30 m

Final Answer

The height of the tower is 30 m, so the correct option is B.