In DeltaKLM,m=98 inches, l=95 inches and /_L=114^(@). Find all possible values of /_M, to the nearest degree. Answer:

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In  DeltaKLM,m=98 inches,  l=95 inches and  /_L=114^(@). Find all possible values of  /_M, to the nearest degree. Answer:

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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 = 98 inches, l = 95 inches, and angle L = 114 degrees. Plugging these into the equation from Step 1 gives us: 98/sin(M) = 95/sin(114°)Solve for sin(M): Solve for sin(M). First, calculate sin(114°) using a calculator: sin(114°) ≈ 0.913545 Now, rearrange the equation to solve for sin(M): sin(M) = (98 * sin(114°)) / 95 sin(M) ≈ (98 * 0.913545) / 95 sin(M) ≈ 89.46741 / 95 sin(M) ≈ 0.9417622Find Angle M: Find the angle M whose sine is approximately 0.9417622. Using a calculator, we find the inverse sine (arcsin) of 0.9417622: M ≈ arcsin(0.9417622) M ≈ 70.53°Check for Second Solution: Check if there is a second possible value for angle M. Since the sine function is positive in both the first and second quadrants, and the sum of angles in a triangle must be 180 degrees, we must check if there is another possible angle M that is less than 180° - 114° = 66°. Since 70.53° is already greater than 66°, there is no second solution within the triangle's angle constraints.Round Angle M: Round the value of angle M to the nearest degree. M ≈ 71° (to the nearest degree)

In $\Delta \mathrm{KLM}, m=98$ inches, $l=95$ inches and $\angle \mathrm{L}=114^{\circ}$ . Find all possible values of $\angle \mathrm{M}$ , to the nearest degree. $\newline$ Answer:

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In ΔKLM,m=98 \Delta \mathrm{KLM}, m=98 ΔKLM,m=98 inches, l=95 l=95 l=95 inches and ∠L=114∘ \angle \mathrm{L}=114^{\circ} ∠L=114∘. Find all possible values of ∠M \angle \mathrm{M} ∠M, to the nearest degree.\newlineAnswer:

In $\Delta \mathrm{KLM}, m=98$ inches, $l=95$ inches and $\angle \mathrm{L}=114^{\circ}$ . Find all possible values of $\angle \mathrm{M}$ , to the nearest degree. $\newline$ Answer: