How do you determine the number of possible solutions using the rule of law of sines given Angle A=31.9 degrees, a=30.6, b=37.9?

Question

Elijah Alexander · Accepted Answer

Solve oblique triangle, knowing A = 31.9; a = 30.6 and b = 37.9

Determine angles B and C. #sin B = (b.sin A)/a = (37.9(0.53))/30.6 = 20.09/30.6 = 0.65# -> -> B is equal to 41.03 degrees 180 - A - B = 180 - 31.9 - 41.03 = 107.07 degrees is Angle C. #c = a(sin C/sin A) # = 30.6(0.96/0.53) = 30.6( 1.81) = 55.43

Samantha Abate · Answer

undefined To determine the number of possible solutions using the rule of law of sines given Angle A=31.9 degrees, a=30.6, b=37.9, you would first calculate the sine of angle A, denoted as sin(A), using the given angle measurement. Then, you would calculate the ratios of the lengths of the sides to their corresponding angles, denoted as sin(a)/a and sin(b)/b, using the given side lengths.

Next, compare sin(A) to sin(a)/a and sin(b)/b. If sin(A) is greater than or equal to sin(a)/a and sin(b)/b, there is one possible solution, which forms an acute triangle. If sin(A) is less than sin(a)/a or sin(b)/b, there are two possible solutions: one acute triangle and one obtuse triangle.

In this specific case, calculate sin(A) using the given angle measurement of A=31.9 degrees. Then, calculate sin(a)/a and sin(b)/b using the given side lengths a=30.6 and b=37.9. Compare sin(A) to sin(a)/a and sin(b)/b to determine the number of possible solutions.