Check point 7.3-7.4

7.3 P 453-4

#4 #16

7.4 P 461

#4

# 8

Geometry

Section 7.5 & 7.6

I can find the sin, cos, and tan ratios given the side of a right triangle.

SOH CAH TOA

Sine, Cosine, Tangent Ratios

EXAMPLE 1 Find sine ratios

Find sin S and sin R. Write each answer as a fraction and as a decimal rounded to four places.

SOLUTION

sin S = opp. Shyp

= RTSR = 63

65 0.9692

sin R = opp. Rhyp

= STSR = 16

65 0.2462

EXAMPLE 2 Find cosine ratios

Find cos S and cos R. Write each answer as a fraction and as a decimal rounded to four places.

SOLUTION

cos S = adj. Shyp

= STSR = 16

65 0.2462

cos R = adj. Rhyp

= RTSR = 63

65 0.9692

EXAMPLE 1 Find tangent ratios

Find tan S and tan R. Write each answer as a fraction and as a decimal rounded to four places.

SOLUTION

tan S =opp S

adj S= RTST

= 80 18

= 40 9

4.4444

tan R =opp R

adj R= STRT

= 18 80

= 9 40

0.2250=

EXAMPLE 6 Use a special right triangle to find a sine and cosine

Use a special right triangle to find the sine and cosine of a 60o angle.

SOLUTION

Use the 30o - 60o - 90o Triangle Theorem to draw a right triangle with side lengths of 1, and 2. Then set up sine and cosine ratios for the 60o angle.

3

sin 60o =opp. hyp.

=3

20.08660

cos 60o =adj. hyp.

=21

0.5000=

2. Find the values of x (find the missing leg) and y (find the hypotenuse).

yy

Solutions for Check point 7.3-7.4

7.3 P 453

#4 #16

7.4 P 461

#4

# 8

∆KML ~ ∆MNL ~ ∆KNM

L

K

M

MN

L

KMN x

x

x

x

6

36

9

4

2

10

25

225

2

hyp

hyp

hyp

leghyp

18

92

2

y

y

legshorthyp

39

3

x

legshortleglong

WARM UP: Lesson 7.6, For use with pages 473-480

2. Name the leg opposite X.

Use this diagram for Exercises 1-4.

1. Name the hypotenuse.

ANSWER YZ

ANSWER XZ

3. Name the leg adjacent to X.

ANSWER XY

Check point 7.4 -7.5-6

7.4

7.5-6

1) Draw and Label the sides on a 45° – 45° – 90° Triangle

2) Draw and Label the sides on a 30° – 60° – 90° Triangle

4) List the trigonometric ratios for sine, cosine, and tangent

3) Draw and label the sides of the right triangle with respect to A.

Hint: Opposite, Adjacent, Hypotenuse

A

C B

Geometry

Section 7.5 & 7.6 Combined

(I can draw a picture and solve a story problem using sin, cos, and tan)

1. Find sin J , cos K, tan K. Round to four decimal places.

EXAMPLE 3 Use a trigonometric ratio to find a hypotenuse

DOG RUN

You want to string cable to make a dog run from two corners of a building, as shown in the diagram. Write and solve a proportion using a trigonometric ratio to approximate the length of cable you will need.

55

EXAMPLE 3 Use a trigonometric ratio to find a hypotenuse

SOLUTION

sin 35o =opp hyp Write ratio for sine of 35o.

sin 35o = 11x

Substitute.

x sin 35o = 11 Multiply each side by x.

x = 11. sin 35o Divide each side by tan. 35o

x 11. 0.5736

Use a calculator to find tan. 35o

x 19.2 Simplify.

ANSWER

You will need a little more than 19 feet of cable.

EXAMPLE 4 Find a hypotenuse using an angle of depression

SKIING

You are skiing on a mountain with an altitude of 1200 meters. The angle of depression is 21o. About how far do you ski down the mountain?

EXAMPLE 4 Find a hypotenuse using an angle of depression

SOLUTION

sin 21oWrite ratio for sine of 21o.

sin 21o Substitute.

x sin 21o = 1200 Multiply each side by x.

x = 1200. sin 21o Divide each side by sin 21o

x 1200. 0.3584

Use a calculator to find sin 21o

x 3348.2 Simplify.

opp hyp=

1200x=

ANSWER

You ski about 3348 meters down the mountain.

A six-meter-long ladder leans against a building. If the ladder makes an angle of 60° with the ground, how far up the wall does the ladder reach? How far from the wall is the base of the ladder?

Launch

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