Use trig ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Use sine to find a missing opposite side or hypotenuse in a right triangle
Problem
Use \(\text{sine}\) to find the missing side: angle \(30^{\circ}\), hypotenuse \(10\), opposite \(x\)
Big Picture
What this problem is really about
Sine directly relates the opposite side and hypotenuse for the stated reference angle. We’ll assign those roles, write opposite over hypotenuse in the correct order, substitute the exact special-angle value, solve for the missing length, and check the original ratio.
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