CPM 4.2.4

CPM 4.2.4

How can I use trig ratios?

Trigonometric Applications

Throughout this chapter, you have developed new tools to help you determine the length of any side or the measurement of any angle of a right triangle. Trigonometric ratios, as well as the Pythagorean Theorem, give you the powerful ability to solve problems involving right triangles. Today you will apply this knowledge to solve some everyday situations. 

Trigonometric Applications

As you are working with your team on the problems below, be sure to draw and label a diagram and determine which trigonometric ratio to use before you start solving.

4-89, CLIMBING IN YOSEMITE

David and Emily are climbing El Capitan, a big cliff wall in Yosemite National Park. David is on the ground holding the rope attached to a carabiner (a rope “pulley” that is on the wall) above Emily as she climbs. When Emily stops to rest, David wonders how high she has climbed.

4-89, CLIMBING IN YOSEMITE

The rope is attached to his waist, about 3 feet off the ground, and he has let out 48 feet of rope which goes up to the carabiner and then back down the wall to Emily’s harness. The rope at David’s waist makes a $55\degree$ angle with the ground and he is standing 20 feet away from the base of the wall. Draw a picture to represent the situation.

Multiple Choice

4-89, part a: Assuming that the rope is taut (pulled tight), approximately how long is the rope between David and the carabiner above Emily?

• 24.4 ft.

• 34.9 ft.

• 14.0 ft.

• 11.5 ft.

• 16.4 ft.

Multiple Choice

4-89, part b: How high up the wall has Emily climbed?

• 19.4 ft.

• 14.5 ft.

• 31.6 ft.

• 28.6 ft.

• 16.4 ft.

4-90

The Bungling Brothers Circus is in town and you are part of the crew that is setting up its enormous tent. The center pole that holds up the tent is 70 feet tall. To keep it upright, a support cable needs to be attached to the top of the pole so that the cable forms a  $60\degree$  angle with the ground. Draw a picture to represent the situation.

Multiple Choice

4-90, part a: How long is the cable?

• 80.8 ft.

• 140.0 ft.

• 40.4 ft.

• 60.6 ft.

• 35.0 ft.

Multiple Choice

4-90, part b: How far from the pole should the cable be attached to the ground?

• 80.8 ft.

• 140.0 ft.

• 40.4 ft.

• 60.6 ft.

• 121.2 ft.

4-91

Nathan is standing in a meadow, exactly 185 feet from the base of El Capitan. At 11:00 a.m., he observes Emily climbing up the wall and determines that his angle of sight up to Emily is about  $60\degree$  . Draw a picture of the situation.

Multiple Choice

4-91, part a: If Nathan’s eyes are about 6

feet above the ground, about how high is Emily at 11:00 a.m.?

• 32.1 ft.

• 182 ft.

• 32.6 ft.

• 1065.4 ft.

• 38.6 ft.

Multiple Choice

4-91, part b: At 11:30 a.m., Emily has climbed some more, and Nathan’s angle of sight to her is now  $25\degree$  . How far has Emily climbed in the past 30
 minutes?

• 47.9 ft.

• 178.7 ft.

• 49.6 ft.

• 690.4 ft.

• 55.6 ft.

Multiple Choice

4-91, part c: If Emily climbs 32 feet higher in ten more minutes, at what angle will Nathan have to look in order to see Emily?

•  $10.0\degree$  
  

•  $80.0\degree$  

•  $9.8\degree$  

•  $34.8\degree$  

•  $35\degree$