RIGHT TRIANGLE TRIG » how to solve right triangles + SOH CAH TOA | Math Hacks

Brett shows you how to solve for missing sides and angles of a right triangle using trigonometric functions (Sine, Cosine, and Tangent, aka soh cah toa) and how to find the missing sides of a right triangle with trigonometry basics including the Pythagorean Theorem.

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SKIP AHEAD »
Example 1 » 1:10
What is SOH CAH TOA? » 2:25
Solve for the missing side using Tan » 5:35
How to plug trig functions into phone calculator » 6:58
Solve for hypotenuse using Cos » 8:35
Solve using the Pythagorean Theorem » 11:35
Find the missing angle » 12:25
Example 2 » 14:21

TO SOLVE FOR MISSING SIDES OF A RIGHT TRIANGLE »
To "solve a right triangle," you have to find all the missing sides and missing angles of the given triangle. To use this approach you need to be given at least one angle in addition to the right angle and one of the side lengths. If you have that information then you are free to use the trigonometric functions: Sine, Cosine, Tangent to solve for the missing side lengths.

To remember the trig ratios for sine, cosine, and tangent, use the memory aid "SOH CAH TOA". Working from the perspective of the angle you are given, choose the function that has both the side you are given and the side you want to solve for. To find the remaining side you can repeat the process of choosing a trig function and solving the equation or you can use use the Pythagorean Theorem ("a squared plus b squared equals c squared").

TO FIND THE MISSING ANGLE »
Remember that in (Euclidean) geometry, there are always 180 degrees in a triangle. Since we already know one angle in addition to the right angle, we can use this fact to solve for the third angle. Simply sum the two known angles and subtract from 180 to get the final angle.

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