Start by identifying the hypotenuse of the right triangle. Then find the sides that are opposite and adjacent to ∠ B.
lsin B=sqrt(57)/11
lcos B=8/11
ltan B=sqrt(57)/8
Practice makes perfect
For the given right triangle, we want to write the ratios for the sine, cosine, and tangent of ∠ B. Let's start by identifying the hypotenuse of the triangle and the sides that are opposite and adjacent to ∠ B.
We see that the length of the hypotenuse is 22. The length of the side adjacent to ∠ B is 16 and the length of the side opposite to ∠ B is 2sqrt(57). With this information, we can find the desired ratios.
Ratio
Definition
Value
sin B
Length of leg opposite∠ B/Length of hypotenuse
2sqrt(57)/22=sqrt(57)/11
cos B
Length of leg adjacent∠ B/Length of hypotenuse
16/22=8/11
tan B
Length of leg opposite∠ B/Length of leg adjacent∠ B
