1. Check point
7.3 P 453-4
# #16
7.4 P 461 #4
# 8

2. Geometry
Section 7.5 & 7.6
I can find the sin, cos, and tan ratios given the side of a right triangle.

4. Sine, Cosine, Tangent Ratios
SOH CAH TOA

5. 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 =
opp. S
hyp
sin S = RT SR = 63 65
0.9692 =
opp. R
hyp
sin R = ST SR = 16 65
0.2462

6. 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 =
adj. S
hyp
cos S = ST SR = 16 65
0.2462 =
adj. R
hyp
cos R = RT SR = 63 65
0.9692

7. 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 =
opp S
adj S =
RTST =
80 18 =
40 9
tan S
4.4444 =
opp R
adj R =
STRT =
18 80 =
9 40
tan R
0.2250 =

8. 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 2
cos 60o =
adj. hyp. 2 1
0.5000 =

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

10. Solutions for Check point 7.3-7.4
# #16
∆KML ~ ∆MNL ~ ∆KNM L L M N K N M M K
7.4 P 461 #4
# 8

11. WARM UP: Lesson 7.6, For use with pages 473-480
Use this diagram for Exercises 1-4.
1. Name the hypotenuse.
ANSWER XZ
2. Name the leg opposite X.
ANSWER YZ
3. Name the leg adjacent to X.
ANSWER XY

12. Check point
7.4
1) Draw and Label the sides on a ° – 45° – 90° Triangle
2) Draw and Label the sides on a ° – 60° – 90° Triangle
7.5-6
3) Draw and label the sides of the right triangle with respect to A.
4) List the trigonometric ratios for sine, cosine, and tangent
Hint: Opposite, Adjacent, Hypotenuse A C B

13. Geometry Section 7.5 & 7.6 Combined
(I can draw a picture and solve a story problem using sin, cos, and tan)

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

15. Use a trigonometric ratio to find a hypotenuse
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

16. Use a trigonometric ratio to find a hypotenuse
EXAMPLE 3
Use a trigonometric ratio to find a hypotenuse
SOLUTION
sin 35o =
opp hyp
Write ratio for sine of 35o.
sin 35o = 11 x
Substitute.
x sin 35o =
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.

18. 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?

19. Find a hypotenuse using an angle of depression
EXAMPLE 4
Find a hypotenuse using an angle of depression
SOLUTION
opp hyp =
sin 21o
Write ratio for sine of 21o.
1200 x =
sin 21o
Substitute.
x sin 21o =
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.
ANSWER
You ski about 3348 meters down the mountain.

20. A six-meter-long ladder leans against a building
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?

21. Launch