Sketch a diagram describing the given situation. Then recall the definition of tangent.
D
Practice makes perfect
We are given that Ryan wanted to know the height of a cell-phone tower, which we will call h. We also know that he is 5 feet tall, he walked 80 feet from the base of the tower, and the angle of elevation to the top of the tower is 54^(∘). Let's sketch a diagram describing the given situation.
First, we should evaluate the difference between height of the tower and the height of Ryan. Let x represents this difference.
To find the value of x, we can use one of the trigonometric ratios Let's recall that the tangent of ∠ A is the ratio of the leg opposite ∠ A to the leg adjacent ∠ A. Using this definition, we can create an equation for tan 54^(∘).
tan 54^(∘)=x/80
Let's solve the above equation.
The value of x is approximately 110 feet. Let's add this information to our diagram.
Finally, the value of h is the sum of Ryan's height and the difference between the height of the cell-phone tower and Ryan.
h=5+ 110=115
The height of the cell-phone tower is approximately 115 feet. This corresponds with answer C.
