For triangle ABC, angle A = 26 degrees, a = 7 cm, b = 15 cm. Determine ALL possible values for c. Round your final answer.

Question

Apparently there might be more than one answer

Answer 1

Gautham:

You are right to think there could be more than one answer. For SSA (side-side-angle) trig problems, there could be 0 solution, 1 solution, or 2 solutions.

Use the law of sines to find ∠B.

sin(∠A)/a = sin(∠B) / b or sin(∠B) = (b*sin(∠A))/a = (15*sin(26))/7 = 0.939366

So ∠B = sin^-1(0.939366) = 69.9

Since ∠A+∠B+∠C = 180, if ∠B = 69.9, ∠C = 84.1

In this case use law of sines again, sin(∠B)/b = sin(∠C)/c so c = (b*sin(∠C))/sin(∠B) = (15*sin(84.1))/sin(69.9) = 15.88

However, ∠B = 180 - 69.9 = 110.1 is also a possibility

In this case ∠A = 26, ∠B=110.1, ∠C=43.9.

Use the same method to determine b and c in this case. Let me know if you need help!

So you have two triangles!