2.4 Trigonometric Ratios
When solving for a triangle, sometimes we are given an angle and a side length instead of two
sides. We can still solve for this triangle using trigonometric ratios.
Investigation
Complete the table based on the provided triangle:
Angles
Sin (36.9) =
Cos (36.9) =
Tan (36.9) =
Lengths
Opposite of
Adjacent to
Angle D
Angle D
Ratios
Hypotenuse
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡
𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡
Compare the two tables. Which trigonometric functions are the same to which ratios?
Key Idea: Trigonometric Ratios
sin ∅ =
cos ∅ =
tan ∅ =
1
We use “SOH-CAH-TOA” to help us remember the Ratios
SOH
is short for
Sine = Opposite/Hypotenuse = O/H
CAH
is short for
Cosine = Adjacent/Hypotenuse = A/H
TOA
is short for
Tangent = Opposite/Adjacent = O/A
Trigonometry Ratios to Solve for Missing Sides
Example 1: Solve for the missing side
Example 2: Solve for the missing side
Example 3: Solve for the missing side
Example 4: Solve for the missing side
Homework: pg. 71 #2(odd), 3-5
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