Trigonometric Ratios
Schedule
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Goal
Review
Problems
Discussion
Word problems
Discussion
Poll: Lesson Feedback
Questions?
Learning Log
Extra Time? Extension Activity
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SOLUTIONS
Sine
Cosine
Tangent
Did you recognize other
methods or "shortcuts"
to use in any of the
problems?
If so, explain.
Rock Climbing
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
karabiner (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.
David’s Question
The rope is attached to his
waist, about 3 feet off of
the ground, and he has let
out 48 feet of rope which
goes up to the karabiner
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.
Draw It
Assuming that the rope is taut (i.e., pulled tight),
approximately how long is the rope between David and the
karabiner above Emily?
Possible Solution
She wrote & solved an equation. Her work is
shown below. Explain what she did in each
step.
Ziv solved it differently. He used the equation to
the below. Explain why they both got the answer
correct.
Did you find the same value for y using
both cosine and sine?
Yes
No
Explain how you know which trigonometric ratio to
use. Be sure to include examples!
Based off of this lesson, how comfortable do you
feel identifying and applying trigonometric ratios?
Very comfortable
Comfortable
Somewhat comfortable
Not comfortable
What questions do you still have about
trigonometric ratios or do you just want more
practice?
Extension
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Can we find the degree of an angle with the
trig ratios we currently have?
Yes
No
From the ratio of side lengths, which angles
can you find?
How can you use information about
the side lengths to help you figure
out the reference angle?