The sine of ∠ K is the ratio of the length of the leg opposite ∠ K to the length of the hypotenuse.
sin K=opposite/hypotenuse ⇒ sin K =8/22
By the definition of the inverse sine, the inverse sine of 822 is the measure of ∠ K. To find it, we have to use a calculator.
To find m∠ J, recall that the acute angles of a right triangle are complementary. Therefore, m ∠ J and m ∠ K add to 90.
m ∠ J + m ∠ K = 90
Now, we can substitute the rounded measure of ∠ K in our equation and find the measure of ∠ J.
m ∠ J + 21 = 90 ⇔ m ∠ J ≈ 69
Side Lengths
Finally, we can find the measure of KL. To do it, we can use the Pythagorean Theorem.
(JL)^2 + (KL)^2 = (JK)^2
Let's substitute the known lengths, JL = 8 and JK= 22, into this equation to find KL.
