Final answer:
To find the length of side L in triangle KLM, use the Law of Sines with the given side and angles, calculate the third angle K, and use the formula to solve for L, rounding to the nearest tenth.
Step-by-step explanation:
You are looking to find the length of side L in triangle KLM. Given that side k is 1.2 cm, angle m/L is 93° and angle M is 6°, we can find the length of L using the Law of Sines. This law states that the ratio of the length of a side to the sine of its opposite angle is the same for all sides and angles in a triangle. The formula is a/sin(A) = b/sin(B) = c/sin(C), where a, b, and c are the sides of the triangle and A, B, and C are the opposite angles.
First, we need to find the third angle of the triangle, angle K. Since the sum of all angles in a triangle equals 180°, angle K can be found by subtracting the sum of the other two angles from 180°. Angle K = 180° - 93° - 6° = 81°.
Now we can use the Law of Sines: 1.2 cm / sin(93°) = L / sin(6°). We rearrange the formula to solve for L, which gives us L = 1.2 cm (sin(6°) / sin(93°)). After performing the calculations, round the result to the nearest tenth of a centimeter as required.