Trigonometry of a Right Triangle

Geometry

Mr. Belanger

Parts of a Right Triangle

Theta (angle measure)

Opposite

Adjacent

Hypotenuse Always longest side (opposite from right angle)

All the way on other side of triangle

Leg next to reference angle

Parts of a Right Triangle

A

BC

40

What side is adjacent, opposite and hypotenuse for given theta?

SIN

SIN ()= hypotenuse

opposite

COS

COS () =hypotenuse

adjacent

TAN

TAN () = adjacent

opposite

Matching Sides

SIN=

COS =

TAN =

c

b

c

a

a

b

Mnemonic Device

S O H C A H T O AIN

PPOSITE

YPOTENUSE

OS

DJACENT

YPOTENUSE

AN

PPOSITE

DJACENT

Examples:

FIND X

SIN (45) = X/400

400 • SIN (45) = X

282.8 miles = X

Examples:

56

How far is ladder from wall?

P

Another Way???

Or find other angle and use another relationship.

12)56cos(

P

P )56cos(12

mP 7.6

P

10)56tan(

Examples:

Find

COS () = 8/10

Use COS-1 (8/10) = 36.9