Start by identifying the hypotenuse of the right triangle. Then find the sides that are opposite and adjacent to ∠ A.
lsin A=4/5
lcos A=3/5
ltan A=4/3
Practice makes perfect
For the given right triangle, we want to write the ratios for the sine, cosine, and tangent. Let's start by identifying the hypotenuse of the triangle and the sides that are opposite and adjacent to ∠ A.
We see that the length of the hypotenuse is 20. The length of the side adjacent to ∠ A is 12 and the length of the side opposite to ∠ A is 16. With this information, we can find the desired ratios.
Ratio
Definition
Value
sin A
Length of leg opposite∠ A/Length of hypotenuse
16/20=4/5
cos A
Length of leg adjacent∠ A/Length of hypotenuse
12/20=3/5
tan A
Length of leg opposite∠ A/Length of leg adjacent∠ A
