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.

Sine, Cosine, Tangent Ratios SOH CAH TOA

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

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

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 =

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 0.08660 cos 60o = adj. hyp. 2 1 0.5000 =

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

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

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

Check point 7.4 -7.5-6 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 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

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.

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

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 = 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?

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 = 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. ANSWER You ski about 3348 meters down the mountain.

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?

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