TRIGONOMETRY BASIC TRIANGLE STUDY: RATIOS: -SINE -COSINE -TANGENT -ANGLES / SIDES SINE LAW: AREA OF A TRIANGLE: - GENERAL -TRIGONOMETRY -HERO’S

BASIC TRIANGLE STUDY

RATIOS c b a A C B The adjacent side is the side next to the reference angle. The opposite side is the side directly across from the reference angle. Remember, it is important to understand that the names of the opposite side and adjacent sides change when you move from one reference angle to the other.

RATIOS SIN ACOS ATAN A

SINE C B A c a b

COSINE B A C a c b

TANGENT B A C c a b

CALCULATOR A B C

ANGLES / SIDES 5 cm x y A BC 50 ⁰

ANGLES / SIDES  FINDING MISSING SIDES USING TRIGONOMETRIC RATIOS IN A RIGHT TRIANGLE (CONTINUED),  Finding the measure of x of side BC opposite to the known angle A, knowing also the measure of the adjacent side to angle A, requires the use of TAN A TAN 30 ⁰ = ⇒ x = 4 · TAN 30 ⁰ = 2.31 cm A B C 4 cm 30 ⁰ x

ANGLES / SIDES  FINDING MISSING ANGLES USING TRIGONOMETRIC RATIOS IN A RIGHT TRIANGLE,  Finding the acute angle A when its opposite side and the hypotenuse are known values require the use of SIN A. SIN A = ⇒ m ∠A = SIN ¯¹ = 53.1 ⁰ A B C 4 5

ANGLES / SIDES  FINDING MISSING ANGLES USING TRIGONOMETRIC RATIOS IN A RIGHT TRIANGLE,  Finding the acute angle A when its adjacent side and the hypotenuse are know values require the use of COS A COS A = ⇒ m ∠ A = COS ¯¹ = 41.4⁰ A B C 4 3

ANGLES / SIDES  FINDING MISSING ANGLES USING TRIGONOMETRIC RATIOS IN A RIGHT TRIANGLE,  Finding the acute angle A when its opposite side and adjacent side are known values requires the use of TAN A TAN A = ⇒ m ∠ A = TAN ¯¹ = 56.3⁰ A B C 3 2

SINE LAW A B C a bc 15 cm x A B C

SINE LAW 10 cm 13 cm A BCx

AREA OF A TRIANGLE BASE HEIGHT L W

AREA OF A TRIANGLE A B C H a bc h

a b c A B C

GENERALTRIGONOMETRIC HERO’S 3.55 cm 12 cm 6 cm 8 cm 12 cm 6 cm 12 cm 8 cm a b c A B C