91Ó°ÊÓ

MODELING WITH MATHEMATICS The top of the slide is 12 feet from the ground and has an angle of depression of \(53^{\circ} .\) What is the length of the slide?

Verify that the segment lengths form \(\square\) a triangle. Is the triangle acute, right, or obtuse? \(10,15,\) and 5\(\sqrt{13}\)

PROBLEM SOLVING You are Lying a kite with 20 Feet of string extended. The angle of elevation from the spool of string to the kite is \(67^{\circ} .\) a. Draw and label a diagram that represents the situation. b. How far off the ground is the kite if you hold the spool 5 feet off the ground? Describe how the height where you hold the spool affects the height of the kite.

In baseball, the lengths of the paths between consecutive bases are 90 feet, and the paths form right angles. The player on first base tries to steal second base. How far does the ball need to travel from home plate to second base to get the player out?

MODELING WITH MATHEMATICS Planes That high speeds and low elevations have radar systems that can determine the range of an obstacle and the angle of elevation to the top of the obstacle. The radar of a plane \([\text { ying at an altitude of } 20,000 \text { feet detects }\) a tower that is \(25,000\) feet away, with an angle of elevation of \(1^{\circ}\) .

REASONING Explain why the expression \(\sin ^{-1}(1.2)\) does not make sense.

USING STRUCTURE The perimeter of rectangle \(A B C D\) is 16 centimeters, and the ratio of its width to its length is \(1 : 3\) . Segment BD divides the rectangle into two congruent triangles. Find the side lengths and angle measures of these two triangles.

Solve the equation. $$\frac{13}{9}=\frac{x}{18}$$

You are on the observation deck of the Empire State Building looking at the Chrysler Building. When you turn \(145^{\circ}\) clockwise, you see the Statue of Liberty. You know that the Chrysler Building and the Empire State Building are about 0.6 mile apart and that the Chrysler Building and the Statue of Liberty are about 5.6 miles apart. Estimate the distance between the Empire State Building and the Statue of Liberty.

Solve the equation. $$\frac{5.6}{12.7}=\frac{4.9}{x}$$