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IM 2 Lesson 4.2.4
4-89. CLIMBING IN YOSEMITE
Objective: 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.
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. 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° angle with the ground and he is standing 20 feet away
from the base of the wall.
a. Assuming that the rope is taut (pulled tight), approximately how long is the rope between David and the
carabiner above Emily?
b. How high up the wall has Emily climbed? Describe your method.
