8.3 Ratios in Right Triangles

To find trig ratios using right triangles

To solve problems using trig ratios

trigonometry- the word comes from 2 Greek words trigon-meaning triangle

metron meaning measure.

Sinopposite

hypotenuse Cos

adjacent

hypotenuse Tan

opposite

adjacent

A ratio of the lengths of sides of a right triangle .

hypotenuse

A

BCA

djac

ent

opposite

Watch this video...

IN

pposi te

ypotenuse

OS

djacent

AN

ypotenuse

pposi te

djacent

Find sin A, cos A, tan A, sin B, cos B, and tan B. Express each ratio as a fraction and as a decimal

A

B

C 12

13

5

sin .A 5

130 385 cos .A

12

13923 tan .A

5

12417

sin .B 12

13923 cos .B

5

13385 tan .B

12

52 4

Find the value of each ratio to the nearest ten-thousandth

sin 7o = .1219 cos 30o = .8660

Find the measure of each angle to the nearest tenth degree

sin A = .7245

A = sin-1 .7245A = 46.4o

tan C = 9.4618

C = 84o

Find x

63o

20

x

determine the relationship between the given angle and the sides

sin6320

x

.891

1

20x

cross multiply

.891x = 20

solve for x

x = 22.45

Homework

• Put this in your agenda

• Pg 416 17 - 37 odd, 38 - 49