Start by identifying the hypotenuse of the right triangle. Then find the sides that are opposite and adjacent to ∠ A.
lsin A=sqrt(19)/10
lcos A=9/10
ltan A=sqrt(19)/9
Practice makes perfect
For the given right triangle, we want to write the ratios for the sine, cosine, and tangent of ∠ A. 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 18 and the length of the side opposite to ∠ A is 2sqrt(19). With this information, we can find the desired ratios.
Ratio
Definition
Value
sin A
Length of leg opposite∠ A/Length of hypotenuse
2sqrt(19)/20=sqrt(19)/10
cos A
Length of leg adjacent∠ A/Length of hypotenuse
18/20=9/10
tan A
Length of leg opposite∠ A/Length of leg adjacent∠ A
