Warmup: What is wrong with this?

30⁰

8.3 and 8.4 Trigonometric Ratios

Finding Trig Ratios

• A trig ratio is a ratio of the lengths of two sides of a right triangle.

• The word trigonometry is derived from the ancient Greek language and means measurement of triangles.

• The three basic trig ratios are sine, cosine, and tangent.

• Abbreviated as sin, cos, and tan respectively

Trigonometric Ratios

• Let ∆ABC be a right triangle. If you are standing from angle A, the following sides are labeled: opposite, adjacent and hypotenuse

ac

bside adjacent to angle A

Sideoppositeangle A

hypotenuse

A

B

C

sin A =opposite

hypotenuse=

a

c

cos A = adjacent

hypotenuse=

b

c

tan A =opposite

adjacent =

a

b

Trigonometric Ratios

• If you were standing at angle B, you would have to re-label the sides of opposite, adjacent and hypotenuse

sin B =opposite

hypotenuse=

b

c

cos B = adjacent

hypotenuse=

a

c

Tan B =opposite

adjacent =

b

a

ac

bside opposite to angle B

Sideadjacentangle B

hypotenuse

A

B

C

The famous Indian…

SOHCAHTOA

Ex. 1: Find sin, cos and tan of angle S

Ratio S

sin S = opposite

hypotenuse

cosS = adjacent

hypotenuse

tanS = opposite

adjacent 12

13 5

R

T S

Ex.2: Find the sin, cos and tan of angle R

Ratio R

sin R = opposite

hypotenuse

cosR= adjacent

hypotenuse

tanR = opposite

adjacent

12

13 5

R

T S

Using the Inverse

• You can use the sin, cos and tan ratio and calculate it’s inverse, sin-1, cos-1, tan-1 to find the measure of the angle.

• Make sure your calculator is in degree mode!!!

*make note: sin, cos, and tan are ratios.Inverses find angles!!!

Let’s find angle S.

Ratio S

sin S = opposite

hypotenuse

cosS = adjacent

hypotenuse

tanS = opposite

adjacent 12

13 5

R

T S

Now let’s find the angle measure from a previous example

Ratio R

sin R = opposite

hypotenuse

cosR= adjacent

hypotenuse

tanR = opposite

adjacent

12

13 5

R

T S

Examples: Given the triangles below, find the missing angle measure to the nearest degree

26

?

6

8

10 ?

Practice: Solve for the missing variables

1.) 2.)

3.) 4.)

x⁰

12

16

7

26⁰ m

40⁰

9

yz

30

15

(No decimal answers in 4)

p