Let's begin by drawing â–³ JKL and labeling the lengths of the sides. We will also color code the opposite angles and sides.
First, let's check whether the given triangle is a right triangle or not, by using Pythagorean Theorem.
56^2+ 33^2 = 65^2The 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.
