Warm Up April 1st What is the hypotenuse if the leg lengths are a = 72 and b = 30? Simplify 72

EOCT Week 12 #2

Homework Review

What have we learned so far?! Right Triangles What have we learned so far?!

What is the Pythagorean Theorem A²+B²=C²

What are the Pythagorean Triples 3-4-5 5-12-13

Finding Missing Side length A = 300 B=400 C=? C=500

Hint: Rationalize the denominator Simplify Hint: Rationalize the denominator

In a 45-45-90 triangle the ____________are the _______________ Legs are the same

Solve for x 45 x 3 3

What is the area of the hypotenuse? 12 + 20=32 Area=12 Area=20

Solve for x and y x √7 y Y=The same so √7 X= √7•√2=√14

Solve for x 45 3√2 x X=3

Find all the side lengths Legs: 7 and 4 Hypotenuse=√65 Area=49 Area=16

Solve for x 45 3 x 3=x√2

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

45-45-90 Right Triangle x x

30-60-90 Right Triangle a 2a 30 60

30-60-90 Triangles The longer leg is _____ times bigger than the shorter leg. The hypotenuse is _____ times bigger than the shorter leg. The longer leg is √3 times bigger The hypotenuse is 2 times bigger than the shorter leg

Type 1: Given Hypotenuse find the legs

Just Watch Find the values of x and y. Give your answers in simplest radical form. 22 = 2x Hypotenuse = 2(shorter leg) 11 = x Divide both sides by 2. Substitute 11 for x.

#1 You Try! 60 30 x y 20 20=2x (hypotenuse is twice as big as shorter leg) 10=x Y=x√3 (long leg is √3 times bigger than shorter leg) Y=10√3

#2 You Try! Find the values of x and y. Give your answers in simplest radical form. Hypotenuse = 2(shorter leg) Divide both sides by 2. y = 27 Substitute for x.

Type 2: Given long leg find short leg and hypotenuse

Just Watch Find the values of x and y. Give your answers in simplest radical form. Rationalize the denominator. y = 2x Hypotenuse = 2(shorter leg). Simplify.

#1 You Try! 60 30 x y 21=x√3 (long side is √3 larger than short side) X= 21/√3……21√3/3……..7√3 Y=2x (hypotenuse is twice as big as short side) Y=2(7√3) Y=14√3

#2 You Try! Find the values of x and y. Give your answers in simplest radical form. Rationalize the denominator. x = 2y Hypotenuse = 2(shorter leg) Simplify.

Type 3: Given short leg find long leg and hypotenuse

Just Watch Find the values of x and y. Give your answers in simplest radical form. y = 2(5) y = 10 Simplify.

You Try! 60 30 x y 7 X=7√3 (Long leg is √3 times larger than short side) Y=2(7) (Hypotenuse is twice as big as the short side) Y=14

Special Triangles Summary Find the values of the variables. Give your answers in simplest radical form. 1. 2. 3. 4. x = 10; y = 20

Classwork/Homework CW: 30-60-90 Worksheet What you don’t finish is HW *Turn in when finished