Use trig ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Use cosine to find a missing adjacent side or hypotenuse in a right triangle
Problem
Use \(\text{cosine}\) to find the missing side: angle \(60^{\circ}\), hypotenuse \(12\), adjacent \(x\)
Big Picture
What this problem is really about
Cosine is the direct bridge between the adjacent leg and hypotenuse. We’ll label those roles relative to the given angle, keep the hypotenuse in the denominator, insert the exact cosine value, isolate the unknown, and substitute back to verify the side ratio.
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