60-90 TRIANGLESIN A RIGHT TRIANGLE WITH THE OTHER ANGLES MEASURING...

30-60-90 T

^RIANGLES

In a right triangle with the other angles measuring 30 and 60 degrees:

■

The leg opposite the 30-degree angle is half of the length of the hypotenuse. (And, therefore, thehypotenuse is two times the length of the leg opposite the 30-degree angle.)

■

The leg opposite the 60-degree angle is 3times the length of the other leg.

60

°

30

°

Example

7 xyx= 2 · 7 = 14 and y= 73

C

ONGRUENT

Two figures are congruent if they have the same size and shape.

T

RANSLATIONS

,

ROTATIONS

,

AND REFLECTIONS

Congruent figures can be made to coincide (place one right on top of the other), by using one of the followingbasic movements.

TRANSLATION (SLIDE)

ROTATION

REFLECTION (FLIP)

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A C T M AT H T E S T P R A C T I C E

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TrigonometryBasic trigonometric ratios, graphs, identities, and equations are covered in this section.

B

^ASIC

T

RIGONOMETRIC

R

^ATIOS

it

o

p

e

s

sin A=

hy

se

oppositerefers to the length of the leg opposite angle A.

u

n

t

c

a

d

ja

en

cos A=

hy

te

se

adjacentrefers to the length of the leg adjacent to angle A.

i

tan A=

a

t

j

T

RIGONOMETRIC

I

^DENTITIES

sin

²

x+ cos

²

x= 1

si

n

x

tan x=

c

o

s

x

sin 2x= 2sin xcos xcos 2x= cos

²

x−sin

²

x

x

2

x

ta

2

tan 2x=

1

−

P r a c t i c e Q u e s t i o n s

DirectionsAfter reading each question, solve each problem, and then choose the best answer from the choices given.(Remember, the ACT Math Test is different from all the other tests in that each math question contains fiveanswer choices.) When you are taking the official ACT, make sure you carefully fill in the appropriate bub-ble on the answer document.You may use a calculator for any problem, but many problems are done more quickly and easily with-out one.Unless directions tell you otherwise, assume the following:

■

figures may not be drawn to scale

■

geometric figures lie in a plane

■

“line” refers to a straight line

■

“average” refers to the arithmetic meanRemember, the questions get harder as the test goes on. You may want to consider this fact as you paceyourself.