Question

MODELING WITH MATHEMATICS The top of theslide is 12 feet from the ground and has an angle ofdepression of 53°. What is the length of the slide?(See Example 6.)53%12 ft37. MULTIPLE REPRESENTATIONS You are standing ona cliff above an ocean. You see a sailboat from yourvantage point 30 feet above the ocean.a. Draw and label a diagram of the situation.b. Make a table showing the angle of depression andthe length of your line of sight. Use the angles 40°,50°, 60°, 70°, and 80°.c. Graph the values you found in part (b), with theangle measures on the x-axis.d. Predict the length of the line of sight when theangle of depression is 30°.

Answer 1

Given:

The height of the slide from the ground = 12 feet

The angle of depression = 53 degrees

Required:

Find the length of the slide.

Explanation:

The given triangle is the right triangle.

adjacent = 12 ft

we have to find the hypotenuse side.

Let the length of the slide is h ft.

Use the following trigonometric ratio:

$cos\theta=\frac{adj.}{hyp.}$$\begin{gathered} cos53\degree=\frac{12}{h} \\ h=\frac{12}{cos53\degree} \\ h=\frac{12}{0.6018} \\ h=19.94 \\ h\approx20\text{ feet} \end{gathered}$

Final Answer:

The length of the slide is approximately 20 ft.