In DeltaKLM,m=55 inches, l=49 inches and /_L=121^(@). Find all possible values of /_M, to the nearest degree. Answer:

Question

In  DeltaKLM,m=55 inches,  l=49 inches and  /_L=121^(@). Find all possible values of  /_M, to the nearest degree. Answer:

Bytelearn · Accepted Answer

Apply Law of Sines: Use the Law of Sines to find the ratio of the sides to the sines of their opposite angles. The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. That is, for triangle KLM: m/sin(M) = l/sin(L)Substitute Given Values: Substitute the given values into the Law of Sines. We have m = 55 inches, l = 49 inches, and angle L = 121 degrees. Plugging these into the equation from Step 1 gives us: 55/sin(M) = 49/sin(121°)Solve for sin(M): Solve for sin(M). First, calculate sin(121°). Since 121° is in the second quadrant, where sine is positive, we can use a calculator to find: sin(121°) ≈ 0.8572 Now, we can rearrange the equation to solve for sin(M): sin(M) = (55 * sin(121°)) / 49 sin(M) ≈ (55 * 0.8572) / 49 sin(M) ≈ 47.146 / 49 sin(M) ≈ 0.9624Find Angle M: Find the angle M whose sine is approximately 0.9624. Using a calculator, we find that: M ≈ sin^(-1)(0.9624) M ≈ 74.5° (to the nearest degree)Check for Second Solution: Check for possible second solution. Since the sine function is positive in both the first and second quadrants, there could be another possible value for angle M in the second quadrant. However, since angle L is already 121 degrees and the sum of angles in a triangle must be 180 degrees, there is not enough degrees left for angle M to be in the second quadrant. Therefore, there is only one possible solution for angle M.Verify Angle Sum: Verify that the sum of angles in triangle KLM is 180 degrees. Angle K = 180° - (Angle L + Angle M) Angle K = 180° - (121° + 74.5°) Angle K = 180° - 195.5° This would give a negative value for angle K, which is not possible. Therefore, we must have made a rounding error in Step 4. We need to find the exact value of angle M without rounding to ensure the sum of angles is 180 degrees.

In $\Delta \mathrm{KLM}, m=55$ inches, $l=49$ inches and $\angle \mathrm{L}=121^{\circ}$ . Find all possible values of $\angle \mathrm{M}$ , to the nearest degree. $\newline$ Answer:

Full solution

More problems from Sin, cos, and tan of special angles

Related topics

In ΔKLM,m=55 \Delta \mathrm{KLM}, m=55 ΔKLM,m=55 inches, l=49 l=49 l=49 inches and ∠L=121∘ \angle \mathrm{L}=121^{\circ} ∠L=121∘. Find all possible values of ∠M \angle \mathrm{M} ∠M, to the nearest degree.\newlineAnswer:

In $\Delta \mathrm{KLM}, m=55$ inches, $l=49$ inches and $\angle \mathrm{L}=121^{\circ}$ . Find all possible values of $\angle \mathrm{M}$ , to the nearest degree. $\newline$ Answer: