8.3 ratios in right triangles

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

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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