Solving Right Triangles

Pre-Calculus · Axiom Academy

EXAMPLE Solving Right Triangles Find every missing side and angle of a right triangle using SOH-CAH-TOA and the fact that the two acute angles add to 90°. "Solving a right triangle" means finding all of its unknown sides and angles. Here we are given one acute angle and one side: angle and the side opposite it a = 8 . The right angle sits at C . Find the other acute angle B , the adjacent side b , and the hypotenuse c . Nice work — you solved the triangle completely. Given just one angle and one side, every remaining part follows from three tools. Angle-sum shortcut: the two acute angles of a right triangle always add to , so — no trig needed. Pick the ratio by what you have and want: SOH-CAH-TOA — , , . We used sine for c and tangent for b . Result: , , . Check: — the Pythagorean theorem closes. The same playbook solves any right triangle: knowing a side opposite a known angle unlocks the hypotenuse with sine and the adjacent side with tangent, while hands you the last angle for free.

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