13.1 – Solving Right Triangles

Day #1 Objective:Use rules of special right triangles to find the lengths of missing sides.

30°

60°

30-60-90right triangle

45°

45°

45-45-90right triangle

Two Special Right Triangles

In either of these two special right triangles, given one side you can find the remaining two sides.

30-60-90 Right Triangle

30°

60°

s2s

3s

Memorize this!

Understand side lengths in relation to the angle measures.

45°

45°

s

s

45-45-90 Right Triangle

2s

Memorize this!

Understand side lengths in relation to the angle measures.

5x

y

Find the values of x and y.

45°

60°

x

2 y

Helpful Hints:• Label all angles and locate the smallest

side.• Find the value of the smallest side.• Find the value of remaining side(s) from the

smallest slide.

Find the values of x and y.

8

xy45

°

60°

y

18x

Example 1:

Example 2:

9, 9 3x y 8, 8 2x y

Find the values of x and y.

y

x1445

°

60°

y

x5

Example 3:

Example 4:

10 3 5 3,

3 3x y

7 2x y

Find the values of x and y.

x

6y30

°

45°

y

9x

Example 5:

Example 6:

9 22

x y

2 3, 4 3x y

HomeworkComplete all 5 problems on the

worksheet. Show your work!