# Trigonometry: Solving Right Triangles... How? (NancyPi)

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HOW TO SOLVE A RIGHT TRIANGLE: If you have to "solve a right triangle," it just means to find all the missing angles and sides of a triangle. When you have a right triangle and you already know at least one of the angles (other than the right angle) and at least one of the sides, you can solve for the other sides using a trig function: sine, cosine, or tangent. When solving right triangles, you can use the memory trick sohcahtoa (SOH CAH TOA) to remember the trig ratios for sin, cos, and tan. Pick the trig function that includes both the side you already know AND the side you're looking for. You can use algebra to solve for the length of the unknown side, to find the missing side of a triangle. Once you have that side, you have two options for finding the last unknown side. You can either: 1) use another trig function, or 2) use the Pythagorean Theorem formula. Then you will have all the sides. Make sure you have found all the angles inside the triangle so that you've really "solved" the whole triangle. If you know two angles already (one of them is the right angle, 90 degrees), you can find the last unknown angles really quickly. Since all three angles have to add up to 180 degrees, you can subtract the two angles from 180 to find the unknown angle in degrees.

For how to identify adjacent, opposite, and hypotenuse sides of a triangle, and for an introduction to the trigonometric functions sin, cos, and tan, jump to my BASIC TRIGONOMETRY intro video: https://youtu.be/bSM7RNSbWhM

For more of my right triangle trigonometry and other math videos, check out: http://nancypi.com