Objective: To use the sine, cosine, and tangent ratios to
determine missing side lengths in a right triangle. Right Triangle
Trigonometry Sections 9.1 and 9.2
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IN A RIGHT TRIANGLE. There are ratios we can use to determine
side lengths. These ratios are constant, no matter what the lengths
for the sides of the triangle are. These ratios are called
trigonometric ratios. Three of the trigonometric ratios are: Sine
(sin) Cosine (cos) Tangent (tan)
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TRIG RATIOS Hypotenuse B C A SIN= leg opposite of angle,
hypotenuse COS= leg adjacent to angle, hypotenuse TAN= opposite
leg, adjacent leg SOHCAHTOA
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Write the trig ratios for the following: x z y B CA tan A =tan
B= sin A = sin B = cos A =cos B =
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Lets put numbers in Use the triangle to write each ratio. 12 20
G 16 RT sin G = cos G= tan G = sin T= cos T= tan T=
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Example Use the triangle to write each ratio. 60 Z 87 63 Y
X
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If given the angle measure, you can use a trig function to find
a missing side length of a right triangle. x 25 M L Find x. K 57
Which trig ratio relates the given angle, and the 2 sides?? Set up
equation:
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Examples: Find x. 1.2. 58 18 x x 30 4
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Example: To measure the height of a tree, Mrs. Shattuck walked
125 ft. from the tree, and measured a 32 angle from the ground to
the top of the tree. Estimate the height of the tree.
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Example: A 20 ft wire supporting a flagpole forms a 35 angle
with the flagpole. To the nearest foot, how high is the
flagpole?
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Example: You are at the playground, and they just put in an
awesome new slide. The slide is 25 ft long, and it creates a 57
angle with the ground. How high off the ground is the top of the
slide?
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If you need to find an angle in a right triangle given the side
lengths, you use the inverse of the trig function: tan -1, sin -1,
cos -1 tan -1 (.5) = x The angle,x, whose tangent is.5 sin -1
(.7314)=x The angle,x, whose sine is.7314 cos -1 (.5592)=x The
angle,x, whose cosine is.5592
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Fill in the blanks. 1. cos __________ .0175 2. sin __________
.9659 3. tan___________ .2309 In your calculator, enter cos -1
(.0175)
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Find the indicated angle measures. 1. 2. S 41 47 T R 17 41 A
How would you now find the measure of angle T??
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Find the measure of angle A. A 15 32
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Example: A right triangle has a leg 1.5 units long and a
hypotenuse 4.0 units long. Find the measures of its acute angles to
the nearest degree.
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Example: You are 200 ft from the base of a 150 ft building.
What is the angle formed from the found where you are standing to
the top of the building??
