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Finding Trigonometric Ratios for Angle Y in a Right Triangle
Published on April 2, 2026
Trigonometry
Calculate tan Y, cos Y, and sin Y for a right triangle with side lengths 5, 12, and 13 by applying SOH CAH TOA definitions based on the sides opposite and adjacent to angle Y.
Question
Answer
To find the trigonometric ratios for angle
- Opposite side: The side directly across from angle
is , which has a length of . - Adjacent side: The side next to angle
(that is not the hypotenuse) is , which has a length of . - Hypotenuse: The side across from the right angle
is , which has a length of .
Using the trigonometric definitions (SOH CAH TOA):
-
: This is the ratio of the opposite side to the adjacent side. -
: This is the ratio of the adjacent side to the hypotenuse. -
: This is the ratio of the opposite side to the hypotenuse.
Final answers: