trigonometry of a right triangle geometry mr. belanger
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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
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