8-3:8-3:TrigonometryTrigonometry

ObjectivesObjectives To use the sine, cosine, and tangent To use the sine, cosine, and tangent

ratios to determine side lengths and ratios to determine side lengths and angle measures in right trianglesangle measures in right triangles

Trigonometry RatiosTrigonometry Ratios

Trigonometry: The study of the relationship between the sides and the angles of a triangle

Hypotenuse Opposite

Adjacent

A

B

C Tangent of

tan A =

A

Adjacent

Opposite

Sine of

sin A =

A

Hypotenuse

Opposite

Cosine of

cos A =

A

Hypotenuse

Adjacent

SOHCAHTOA

S O H

TOASOHCAH

ine

pposite

ypotenuse

C A Hosine

dJacent

ypotenuse

T O Aangent

djacent

pposite

Examples

200

500 ftx

8 ft

A

15 ft

sin 200 =x

500

x (sin 200) = 500

x = 020sin

500

x ≈ 1,462 ft

tan A =15

8

tan A = 0.5333

p. 510: 1-6, 11-19

x =342.0

500

350

872

SOHCAHTOACalculators in

“degree” mode!!

Using Inverses> You know two sides

> You want to find the measure of one of the acute angles.

S O H

TOASOHCAH

ine

pposite

ypotenuse

C A Hosine

dJacent

ypotenuse

T O Aangent

djacent

pposite

8-3 DAY 2

200

500 ftx

8 ft

A

15 ft

sin 200 =x

500

x (sin 200) = 500

x = 020sin

500

x ≈ 1,462 ft

tan A =15

8

tan A = 0.5333

A = tan-1 0.5333

A ≈ 280

x =342.0

500

SOHCAHTOA

SOHCAHTOA

B = cos-1 0.6631

500 ft754 ft

cos B =754

500

B

B ≈ 480 p.511: 22-27, 34, 35, 59-62