Find the lengths of the missing sides of a triangle if side a is opposite angle A, side b is opposite angle B, and side c is the hypotenuse. sin(B) = 1/√ 7 , a = 8

Answer 1

Since you describe side c as the hypotenuse, I am assuming the triangle is a right triangle. If so, it might look like this:

sin(B) = opp/hyp = b/c = 1/√7. That means b√7 = c

Using the Pythagorean Theorem, a² + b² = c² we can now say:

8² + b² = (b√7)²

64 + b² = 7b²

64 = 6b²

b² = 32/3

b = √32/√3 = √96/3 = 4√6/3

Since c = b√7, then c = 4√42/3

So, summarizing, a = 8, b = 4√6/3, and c = 4√42/3