Question

Help! Given the sample triangle below and the conditions, sin B = 1/2 and a = 20, find the hypotenuse of the triangle.

Answer 1

a hypotenuse is the longest side of a right-angled triangle, the side opposite of the right angle

Answer 2

This is a right triangle, so we can use the definition of sin from SOH CAH TOA:

Sin (of angle) = Opposite side / hypotenuse

Sin of angle B = 1/2 (from problem statement)

Sin of angle B = opposite / hypotenuse = b/c

We know therefore that b/c = 1/2, and we can use that with a = 20 and the Pythagorean theorem to find b and c.

Answer 3

Solve \[\frac{b}{c} = \frac{1}{2}\]for \(b\) in terms of \(c\). Then write out \[a^2+b^2=c^2\]substitute in your value for \(b\) in terms of \(c\) on the left hand side, and the value of \(a=20\) on the left hand side. You should then have an equation in terms only of \(c\) to solve, and the positive answer will be the length of the hypotenuse.