Check point 7.3-7.4

1. 7.3 P 453-4 #4 #16 Check point 7.3-7.4 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. opp. S 63 16 RT ST = = = 0.9692 hyp SR 65 SR 65 opp. R = = = 0.2462 hyp EXAMPLE 1 Find sine ratios Find sin Sand sin R. Write each answer as a fraction and as a decimal rounded to four places. SOLUTION sin S sin R

6. adj. S 16 63 ST RT = = = 0.2462 hyp SR 65 SR 65 adj. R = = = 0.9692 hyp EXAMPLE 2 Find cosine ratios Find cos Sand cos R. Write each answer as a fraction and as a decimal rounded to four places. SOLUTION cos S cos R

7. adj R opp S adj S opp R RTST 40 9 80 18 = = = = = 4.4444 STRT 9 40 18 80 = = = = 0.2250 EXAMPLE 1 Find tangent ratios Find tan Sand tan R. Write each answer as a fraction and as a decimal rounded to four places. SOLUTION tanS tanR

8. 3 3 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 60oangle. adj. hyp. opp. hyp. sin60o = 0.08660 = 2 1 cos60o = = 0.5000 = 2 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

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

10. 7.3 P 453 #4 #16 ∆KML ~ ∆MNL ~ ∆KNM L L M N K N M M K Solutions for Check point 7.3-7.4 7.4 P 461 #4 # 8

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

12. 7.4 1) Draw and Label the sides on a 45° – 45° – 90° Triangle 2) Draw and Label the sides on a 30° – 60° – 90° Triangle Check point 7.4 -7.5-6 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. 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. EXAMPLE 3 Use a trigonometric ratio to find a hypotenuse DOG RUN 55

16. sin 35o = opp hyp 11 sin 35o = x xsin 35o = 11 x = x 11. 11. sin35o 0.5736 ANSWER x 19.2 You will need a little more than 19 feet of cable. EXAMPLE 3 Use a trigonometric ratio to find a hypotenuse SOLUTION Write ratio for sine of 35o. Substitute. Multiply each side by x. Divide each side by tan. 35o Use a calculator to find tan. 35o Simplify.

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. = opp hyp 1200 = x xsin 21o 1200. x = sin21o 1200. x 0.3584 ANSWER x 3348.2 You ski about 3348 meters down the mountain. EXAMPLE 4 Find a hypotenuse using an angle of depression SOLUTION sin 21o Write ratio for sine of 21o. sin 21o Substitute. = 1200 Multiply each side by x. Divide each side by sin 21o Use a calculator to find sin21o Simplify.

20. 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?

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