In /_\KLM,k=550cm,m=540cm and /_M=74^(@). Find all possible values of /_K, to the nearest 1oth of a degree. Answer:

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In  /_\KLM,k=550cm,m=540cm and  /_M=74^(@). Find all possible values of  /_K, to the nearest 1oth of a degree. Answer:

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Given triangle KLM: We are given a triangle KLM with sides k=550cm, m=540cm, and angle M=74 degrees. We want to find the possible values of angle K. We can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.Law of Sines: First, we write the Law of Sines for our triangle: (sin(K)/m) = (sin(M)/k)Write Law of Sines: We plug in the known values: (sin(K)/540) = (sin(74 degrees)/550)Plug in values: Now we solve for sin(K): sin(K) = (sin(74 degrees)/550) * 540Solve for sin(K): We calculate the value of sin(74 degrees) using a calculator: sin(74 degrees) ≈ 0.9613Calculate sin(74 degrees): We substitute this value into our equation: sin(K) = (0.9613/550) * 540Substitute value: We perform the calculation: sin(K) ≈ (0.9613/550) * 540 ≈ 0.9419Perform calculation: Now we find the angle K whose sine is approximately 0.9419. We use the inverse sine function (arcsin) on a calculator: K ≈ arcsin(0.9419)Find angle K: We calculate the value of K: K ≈ 70.5 degreesCalculate value of K: However, since the sine function is positive in both the first and second quadrants, there is another possible value for angle K. It is the supplement of 70.5 degrees, which is 180 degrees - 70.5 degrees.Find supplement of K: We calculate the supplement of K: K ≈ 180 degrees - 70.5 degrees ≈ 109.5 degreesCalculate supplement of K: We now have two possible values for angle K: 70.5 degrees and 109.5 degrees. However, we must check if these values are valid by ensuring that the sum of angles in a triangle is 180 degrees.Check validity of values: We add the known angle M and both possible values of angle K to see if they sum to 180 degrees: 74 degrees + 70.5 degrees + angle L = 180 degrees 74 degrees + 109.5 degrees + angle L = 180 degreesAdd angles: We solve for angle L in both cases: For K = 70.5 degrees: angle L = 180 degrees - 74 degrees - 70.5 degrees ≈ 35.5 degrees For K = 109.5 degrees: angle L = 180 degrees - 74 degrees - 109.5 degrees ≈ -3.5 degreesSolve for angle L: The second case gives us a negative value for angle L, which is not possible in a triangle. Therefore, the only valid value for angle K is 70.5 degrees.

In $\triangle \mathrm{KLM}, k=550 \mathrm{~cm}, m=540 \mathrm{~cm}$ and $\angle \mathrm{M}=74^{\circ}$ . Find all possible values of $\angle \mathrm{K}$ , to the nearest $10$ th of a degree. $\newline$ Answer:

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In △KLM,k=550 cm,m=540 cm \triangle \mathrm{KLM}, k=550 \mathrm{~cm}, m=540 \mathrm{~cm} △KLM,k=550 cm,m=540 cm and ∠M=74∘ \angle \mathrm{M}=74^{\circ} ∠M=74∘. Find all possible values of ∠K \angle \mathrm{K} ∠K, to the nearest 101010th of a degree.\newlineAnswer:

In $\triangle \mathrm{KLM}, k=550 \mathrm{~cm}, m=540 \mathrm{~cm}$ and $\angle \mathrm{M}=74^{\circ}$ . Find all possible values of $\angle \mathrm{K}$ , to the nearest $10$ th of a degree. $\newline$ Answer: