Let's consider the given diagram. We will use the same color for a side and its opposite vertex. This will help us use the Law of Cosines and later the Law of Sines.
First, we can tell that this is not a right triangle, as the sides do not satisfy the Pythagorean Theorem.
24.6^2+ 29.7^2 ≠ 30.0^2
Let's find the measures of ∠ J, ∠ K, and ∠ L one at a time.
Finding m ∠ J
The lengths of all three sides of the triangle are given. Therefore, we can use the Law of Cosines to find m ∠ J.
j^2=k^2+l^2 -2 k l cos J
Let's substitute j= 29.7, k= 30.0, and l= 24.6 to isolate cos J.
Now that we know the measure of ∠ J, we can find m ∠ K using the Law of Sines.
sin J/j =sin K/k
Let's substitute j= 29.7, m ∠ J ≈ 65, and k= 30, to isolate sin K.
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.
65+ 66 + m ∠ L = 180 ⇔ m ∠ L ≈ 49
Completing the Triangle
With all of the angle measures, we can complete our diagram.
