5.1 Special Right Triangles *You will be able to find the lengths of sides of special right triangles 45-45-90 And 30-60-90

Special Right Triangles Leg:Leg:Hypotenuse Short Leg:Long Leg:Hypotenuse

LEGS ARE THE SAME LENGTH In a 45-45-90 triangle… LEGS ARE THE SAME LENGTH We will use a reference triangle to set up a proportion then solve.

This is our reference triangle for the 45-45-90. 45-45-90 Right Triangle This is what we are given on the EOCT   x x This is our reference triangle for the 45-45-90. 1 Here’s how we change it 1

45-45-90 Right Triangle   x 1 x 1

EX: 1 Solve for x Let’s set up a proportion by using our reference triangle. x 3 1 3 x 3 1 1

EX: 2 Solve for x x 5 1 5 x 5 1 1

EX: 3 Solve for x x 3 45 3 1 1 1 x

30-60-90

We will use a reference triangle to set up a proportion then solve. 30-60-90 Right Triangle 2x 60 60 2 x 1 30   This is our reference triangle for the 30-60-90 triangle. We will use a reference triangle to set up a proportion then solve.

30-60-90 Right Triangle 60 2x 2 x 1 30   This is what we’re given on the formula sheet This is how we change it

Ex: 1 60 8 60 2 x 1 30 30 y y 8 x 8 2 1 2

Solve for x Ex: 2 30 60 2 x 1 24 60 30 24 x 2 1 2x = 24 x = 12

Ex: 3 30 60 2 14 1 y 30 60 x 14 y 14 x 2 2 1 2x = 14 x = 7

Ex: 4 x 60 2 1 60 30 y 30 x y 1 2 y = 10 x = 5