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.
