Special Right Triangles

Special Right Triangles

30°, 60°, and 90° - Special Rule

The hypotenuse is always twice as long as the side opposite the 30° angle.

30°

60°

a

b

c

C = 2a

Special Right Triangles

Example:

30°

60°

6 in

cb

Step 1:

Step 2:

Step 3:

Step 4:

Special Right Triangles

BUT, what if the side across from the 30° angle isn’t given? What if the side that is being looked for isn’t the hypotenuse?

Special Right Triangles

BUT, what if the side across from the 30° angle isn’t given? What if the side that is being looked for isn’t the hypotenuse?

Special Right TrianglesA) When the hypotenuse is given, you can find the side opposite the 30° by solving for a.

c = 2a is the same as

30°

60°

10 ft

Step 1:

Step 2:

Step 3:

Step 4:

c = a 2

Special Right TrianglesB) When the hypotenuse is given, you can also find the side opposite the 60° by solving for a.

30°

60°

10 ft

Step 1:

Step 2:

Step 3:

Step 4:

1.) Find the side opposite of the 30° angle.2.) Use Pythagorean Theorem to solve using the given angle and the found angle in step 1.

Step 1:

Step 2:

Step 3:

Step 4:

Special Right Triangles

45°, 45°, and 90° - Special Rule

Because this type of triangle is also an isosceles triangle, the legs are always congruent. Use pythagorean theorem where the legs are the same measure.

45°

45°

a

b

c

Special Right Triangle

Example:

45°

45°

c

6m

b

Step 1:

Step 2:

Step 3:

Step 4:

Special Right Triangles

YOUR TURN:Go to page 268 of your textbook and complete the “Your Turn” problems.

Special Right Triangles

HOMEWORK: pg. 269, #4-16 (even)