Warm up: Find Side Length CB. CA B 9 4

“Solving” Right Triangles

Things we know about Right triangles: One of the three interior angles is 90 degrees. We can know 6 things about right triangles: 3 interior angles and 3 side lengths If we know two things about a right triangle (other than one of the interior angles is 90 degrees) we can figure everything else out.

Tools We Will Use: Soh Cah Toa Pythagorean Theorem

Example using Pythagorean Theorem b = 100 feet a = 66.7 feet what is the length of C?

Soh Cah Toa

“Solve the Triangle” This means to find all of the angles and all of the sides.

Example 1 Solve the triangle ABC. CA B 25 18

Example 1 Cont… To solve this we will first use Pythagorean Theorem, then Soh Cah Toa. CA B 25 18

Example 1 Cont… C A B 25 18

Example 1 Cont… Now we know side a, but we still need all of the angles in order to solve the triangle. We only need two side lengths in order to find the angles, and it is best to use the two lengths given rather than the one you found incase we made an error. That way, all of our answers won’t be wrong. So we will use 18 and 25 in Soh Cah Toa. CA B

Example 1 Cont… CA B

Example 1 Cont… CA B You finish by solving for B.

Solution C A B ° 90 °

You Try:

Solution B A C °

Trick To find Last Angle Recall, all angles in a triangle sum to 180° So, if you know two angles (which we do since one of them is 90°), you can quickly find the third using this fact. This makes it so that you do not have to use Soh Cah Toa for the last angle.

Homework Pg 494 Problems: 1, 2, 5