2.

Find the value of x to the nearest tenth.

x10

8

warm-up before 6.5:

1.

*** CHECK hw on the blog!!!!

6.5 Sine and Cosine Ratios

Learning Target:I can apply the sine

and cosine ratiosto find side lengths.

(G-SRT.6, 8)

S C TO A OH H A__ __ __

A

B

C

OppHyp

Adj

Name the sides in relationship to ∠A.

In a right Δ,

sine ratio sin ∠ = leg opposite ∠hypotenuse

C

B

A sin ∠A =

In a right Δ,

cosine ratio cos ∠ = leg adjacent ∠hypotenuse

C

B

Acos ∠A =

1. Find sin U and cos U . Write each answer as a simplified fraction and as a decimal rounded to four places.

sin U =

cos U =

16

20

12

W

V

U

sin ∠U =

cos ∠U =

sin ∠W =

cos ∠W =

Write each of the following as a simplified fraction and as a decimalrounded to 4 places.

YOUR TURN:

Legend of Chief

SohCahToa

How can you remember the ratios?

MUST have a calculator!Approximate sin 2˚ to four decimal places.

Approximate cos 14˚ to four decimal places.

Must be in

Degree Mode

2.

Use a sine or cosine ratio, set up an equation using proper notation. Then show work to find the value of x. Round decimals to the nearest tenth.

29˚18

x52 x

42˚

3.

When using trig. ratios, pick the ANGLE first, name the sides, then pick the trig ratio

solve for r:

solve for s:

4. Use a sine or cosine ratio, set up an equation using proper notation. Then show work to find the value of the variables. Round decimals to the nearest tenth.

5. Using trigonometric ratios, set up an equation using proper notation. Then show work to find the value of the variables. Round decimals to the nearest tenth.

y

x 18

35˚

EXIT PROBLEM:You want to put up a fence to make a dog run from two corners of two buildings, as shown in the diagram. Approximate the length of fence you will need.

11 ft

35˚

x ft

Optional

6.5 WorksheetHomework:

S C TO A OH H A__ __ __

Geometry 6.5 Wksht Answers - Sine, Cosine1. sin D = 4/5 = 0.8 2. sin D = _____ = _________

cos D = 3/5 = 0.6 cos D = _____ = _________

3. sin X = 4/5 = 0.8 cos X = 3/5 = 0.6

sin Y = _____ = _________ cos Y = _____ = _________

4. x ≈ 15.8 5. x ≈ 41.1

6. x ≈ ______ 7. x ≈ _______

8. x ≈ 9.5, y ≈ 15.3 9. w ≈ ______ , v ≈ _______

10. h ≈ 109.9 11. x = 5 12. x ≈ 6.9