Use trig ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Use tangent to find a missing leg in a right triangle
Problem
Use \(\text{tangent}\) to find the missing side: angle \(45^{\circ}\), adjacent \(7\), opposite \(x\)
Big Picture
What this problem is really about
Because the known and unknown sides are the two legs, tangent connects them without introducing the hypotenuse. We’ll assign opposite and adjacent relative to the angle, write their ratio, use the exact special-angle tangent, solve for the missing leg, and check the equation.
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