Warm Up April 14th1. What is the hypotenuse if

the leg lengths are a = 6 and b = 4?

2. Simplify

EOCT Week 13 #1

3

3

x

Solve for x

3 2x

45

x

3√245

Solve for x

X=3

x

345

Solve for x

3=x√22

3

223

22

23

You will be able to find the lengths of sides of special

right triangles30-60-90

And45-45-90

45-45-90 Right Triangle

x

x

2x

45

45

30-60-90 Right Triangle

a2a

30

60

a 330 : 60 : 90

a : a 3 : 2a

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

Find the values of x and y. Give your answers in simplest

radical form.

Hypotenuse = 2(shorter leg)22 = 2xDivide both sides by 2.11 = x

Substitute 11 for x.

Just Watch

60

30

x

y

20

#1 You Try!

20=2x (hypotenuse is twice as big as shorter leg)

10=xY=x√3 (long leg is √3 times bigger than shorter leg)

Y=10√3

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.

#2 You Try!

Find the values of x and y. Give your answers in simplest radical

form.

Rationalize the denominator.

Hypotenuse = 2(shorter leg).

Simplify.

y = 2x

Just Watch

y60

30

x 21

#1 You Try!

21=x√3 (long side is √3 larger than short side) X= 21/√3……21√3/3……..7√3Y=2x (hypotenuse is twice as big as short side) Y=2(7√3)Y=14√3

Find the values of x and y. Give your answers in simplest radical

form.

Rationalize the denominator.

Hypotenuse = 2(shorter leg)x = 2y

Simplify.

#2 You Try!

Find the values of x and y. Give your answers in simplest radical form.

Simplify.

y = 2(5)y = 10

Just Watch

60

30x

y7

You Try!

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

Find the values of the variables. Give your answers in simplest radical form.

1. 2.

3. 4.

x = 10; y = 20

SPECIAL TRIANGLES SUMMARY

Finding an angle.(Figuring out which ratio to use

and an inverse trig button.)

111 tancossin

Ex: 1 Figure out which ratio to use. Find x. Round to the nearest tenth.

20 m

40 m

20tan40

26.6o

1 20tan40

x

Tan-1 20 / 40 )

Shrink yourself down and stand where the angle is.

Now, figure out which trig ratio you have and set up the problem.

x

Ex: 2 Figure out which ratio to use. Find x. Round to the nearest tenth.

15 m50 m 15sin

50

17.5 o

1 15sin50

x

Sin-1 15 / 50 )

Shrink yourself down and stand where the angle is.

Now, figure out which trig ratio you have and set up the problem.

x

Ex. 3: Find . Round to the nearest degree.

9

17.29

2.17tan

62

1 17.2tan 9

Ex. 4: Find . Round to the nearest degree.

23

7

237cos

72

1 7cos 23

When we are trying to find a side we use sin, cos, or tan.

When we are trying to find an angle we use

(INVERSE) sin-1, cos-1, or tan-1.