Start with drawing a diagram describing the given situation. Then recall the definition of tangent.
≈ 28.4 meters
Practice makes perfect
Let's begin with sketching a diagram describing the given situation. Since in our exercise we are asked to find the value of x, we need to find the difference between the heights of the slides, which we will call y.
Notice that we can use one of the trigonometric ratios to evaluate the value of y. 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 15^(∘).
tan 15^(∘)=y/50
Let's solve the above equation.
The difference between the height of the taller slide and the height of the shorter slide is approximately 13.4 meters.
Finally, we will evaluate the value of x by adding the height of the smaller slide to the difference between the heights of slides.
x= 13.4+15=28.4
If you are standing at the top of the taller slide, you are approximately 28.4 meters above the ground.
