Introduction to Special Right Triangles

Vocabulary 45-45-90 Triangle: In a 45-45-90 triangle, the hypotenuse is times as long as each leg.

Hints for 45-45-90 Leg to Hypotenuse: MULTIPLY by Hypotenuse to Leg: DIVIDE by Hypotenuse = LEG LEG LEG

Example 1: x = 2 6 2 x = 11∙ 2 x = 11 2 x = 2 3 Find the value of x. a) b) x = 2 6 2 x = 11∙ 2 x = 11 2 x = 2 3

Vocabulary 30-60-90 Triangle: In a 30-60-90 triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is times as long as the shorter leg.

How do you know which is the shorter leg and which is the longer leg??? We know that the hypotenuse is directly across from the 90O angle. The shorter leg is across from the smaller angle (30o) The longer leg is across from the larger angle (60O)

30-60-90 30o Hypotenuse Longer Leg 60o Shorter Leg

You always want to work with the Shorter Leg…it makes it easier! Hints for 30-60-90 Shorter Leg to Hypotenuse: MULTIPLY by 2 Hypotenuse to Shorter Leg: DIVIDE by 2 Shorter Leg to Longer Leg: MULTIPLY by Longer Leg to Shorter Leg: DIVIDE by You always want to work with the Shorter Leg…it makes it easier!

30-60-90 Shorter Leg Longer Leg = Shorter Hypotenuse = 2Shorter 30o

Example 2: Find the values of x and y. x = 4 3 3 x = 4 y = 4 ∙ 2 y = 8

You Try: Find the value of each variable. 1) 2) x = 18 3 ∙ 3 3 x = 9 2 2 y = 6 3 ∙ 2 x = 18 3 3 y = 12 3 x = 9 x = 6 3