In ΔKLM, l = 7.5 cm, mm∠L=57° and mm∠M=113°. Find the length of m, to the nearest 10th of a centimeter
To find the length of side m in triangle KLM, we can use the Law of Sines. The Law of Sines states:
sin(A) / a = sin(B) / b = sin(C) / c
Where A, B, and C are the angles of the triangle, and a, b, and c are the lengths of the sides opposite those angles.
In this case, we have:
sin(∠L) / l = sin(∠M) / m
Plugging in the values we know:
sin(57°) / 7.5 = sin(113°) / m
Now we can solve for m:
sin(57°) = 0.8387
sin(113°) = 0.9781
0.8387 / 7.5 = 0.9781 / m
m = 7.5 * 0.9781 / 0.8387
m ≈ 8.75 cm
Therefore, the length of side m is approximately 8.8 cm to the nearest 10th of a centimeter.