Answer:
∠S possibility is 65 degrees and 115 degrees
Explanation:
∠S + ∠T + ∠U = 180
Substituting the given values, we get:
∠S + ∠T + 79 = 180
Simplifying, we get:
∠S + ∠T = 101
We also know that the sides of a triangle are related to the angles opposite them by the law of sines:
a/sin A = b/sin B = c/sin C
In this case, we can use the following ratio:
ST/sin S = UT/sin U
Substituting the given values, we get:
ST/sin S = UT/sin 79
ST = s = 56 cm
UT = u = 94 cm
Solving for sin S, we get:
sin S = (ST × sin 79) / UT
sin S = (56 × sin 79) / 94
sin S ≈ 0.906
Taking the inverse sine, we get:
∠S ≈ 65 degrees or ∠S ≈ 115 degrees
Therefore, the possible values of ∠S are approximately 65 degrees and 115 degrees, to the nearest degree.