The side lengths satisfy the Pythagorean Theorem. Therefore, we can conclude that the m∠ K will measure 90^(∘). Now, let's find the measures of ∠ J and ∠ L, one at a time.
Finding m ∠ J
Now that we know the given triangle is a right triangle, we can find m ∠ J by using the sine ratio.
sin θ =opposite/hypotenuse
Let's substitute the known side lengths to isolate sin J.
sin J =opposite/hypotenuse ⇔ 56/65
Now we can use the inverse sine ratio to find m ∠ J.
Finally, to find m ∠ L we can use the Triangle Angle Sum Theorem. This tells us that the measures of the angles in a triangle add up to 180.
90+ 59 + m ∠ L = 180 ⇔ m ∠ L ≈ 31
Completing the Triangle
With all of the angle measures, we can complete our diagram.
