WarmUp Exercises Use this diagram for Exercises 1

Warm-Up Exercises Use this diagram for Exercises 1 -4. 1. Name the hypotenuse. ANSWER XZ 2. Name the leg opposite ANSWER YZ X.

Warm-Up Exercises Use this diagram for Exercises 1 -4. 3. Name the leg adjacent to ANSWER XY 4. If XY = 17 and m ANSWER X. 14. 78 X = 41 , find YZ.

Warm-Up 1 Exercises EXAMPLE 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. S hyp = RT SR = 63 65 0. 9692 sin R = opp. R hyp = ST SR = 16 65 0. 2462

Warm-Up Exercises GUIDED PRACTICE for Example 1 Find sin X and sin Y. Write each answer as a fraction and as a decimal. Round to four decimal places, if necessary. ANSWER 8 or 0. 4706, 17 15 or 0. 8824 17 ANSWER 3 or 0. 6, 5 4 or 0. 8 5

Warm-Up 2 Exercises EXAMPLE Find cosine ratios Find cos U and cos W. Write each answer as a fraction and as a decimal. SOLUTION U cos U = adj. to = hyp UV = UW 18 = 3 = 0. 6000 30 5 W cos W = adj. to = hyp WV = UW 24 = 4 30 5 = 0. 8000

Warm-Up 3 Exercises EXAMPLE 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.

Warm-Up 3 Exercises EXAMPLE Use a trigonometric ratio to find a hypotenuse SOLUTION sin 35 o = opp. hyp. sin 35 o = 11 x Substitute. x sin 35 o = 11 Multiply each side by x. x = x x 11 sin 35 o 11 0. 5736 19. 2 Write ratio for sine of 35 o. Divide each side by sin 35 o. Use a calculator to find sin 35 o. Simplify. ANSWER You will need a little more than 19 feet of cable.

Warm-Up Exercises GUIDED PRACTICE for Examples 2 and 3 In Exercises 3 and 4, find cos R and cos S. Write each answer as a decimal. Round to four decimal places, if necessary. ANSWER 0. 6, 0. 8 ANSWER 0. 8824, 0. 4706 5. In Example 3, use the cosine ratio to find the length of the other leg of the triangle formed. ANSWER about 15. 7 ft

Warm-Up 4 Exercises EXAMPLE 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 21 o. About how far do you ski down the mountain?

Warm-Up 4 Exercises EXAMPLE Find a hypotenuse using an angle of depression SOLUTION sin 21 = opp. hyp. Write ratio for sine of 21 o. sin 21 o = 1200 x Substitute. x sin 21 o = 1200 Multiply each side by x. x = 1200 sin 21 o Divide each side by sin 21 o x 1200 0. 3584 Use a calculator to find sin 21 o x 3348. 2 Simplify. o ANSWER You ski about 3348 meters down the mountain.

Warm-Up Exercises GUIDED PRACTICE 6. for Example 4 WHAT IF? Suppose the angle of depression in Example 4 is 28°. About how far would you ski? ANSWER about 2556 m

Warm-Up 5 Exercises EXAMPLE Find leg lengths using an angle of elevation SKATEBOARD RAMP You want to build a skateboard ramp with a length of 14 feet and an angle of elevation of 26°. You need to find the height and length of the base of the ramp.

Warm-Up 5 Exercises EXAMPLE Find leg lengths using an angle of elevation SOLUTION STEP 1 Find the height. opp. sin 26 o = hyp. x 14 sin 26 o = x 6. 1 ANSWER x Write ratio for sine of 26 o. Substitute. Multiply each side by 14. Use a calculator to simplify. The height is about 6. 1 feet.

Warm-Up 5 Exercises EXAMPLE Find leg lengths using an angle of elevation STEP 2 Find the length of the base. adj. cos 26 o = hyp. y 14 cos 26 o = y 12. 6 ANSWER y Write ratio for cosine of 26 o. Substitute. Multiply each side by 14. Use a calculator to simplify. The length of the base is about 12. 6 feet.

Warm-Up 6 Exercises EXAMPLE Use a special right triangle to find a sine and cosine Use a special right triangle to find the sine and cosine of a 60 o angle. SOLUTION Use the 30 o - 60 o - 90 o Triangle Theorem to draw a right triangle with side lengths of 1, 3 , and 2. Then set up sine and cosine ratios for the 60 o angle. o sin 60 opp. = = hyp. 3 2 0. 8660 adj. = hyp. 1 2 = 0. 5000 cos 60 o =

Warm-Up Exercises GUIDED PRACTICE for Examples 5 and 6 7. WHAT IF? In Example 5, suppose the angle of elevation is 35 o. What is the new height and base length of the ramp? ANSWER about 8 feet, about 11. 5 ft 8. Use a special right triangle to find the sine and cosine of a 30 o angle. ANSWER 1 , 2 3 2

Daily Homework Quiz Warm-Up Exercises Use this diagram for Exercises 1 - 3. 1. If x = 4 5 , y = 4 and z = 4 6 , find sin X, sin Y, cos X and cos Y. ANSWER 30 6 cos X = 6 6 sin X = 0. 9129, sin Y = 0. 4082, cos Y = 6 6 30 6 0. 4082, 0. 9129

Daily Homework Quiz Warm-Up Exercises Use this diagram for Exercises 1 - 3. 2. If y = 10 and m ANSWER 38. 6 o Y = 15 , find z to the nearest tenth.

Daily Homework Quiz Warm-Up Exercises Use this diagram for Exercises 1 - 3. If z = 12 and m ANSWER 1. 3 o X = 84 , find y to the nearest tenth.

Daily Homework Quiz Warm-Up Exercises 4. A lamppost is 11 feet tall. If the angle of elevation of the sun is 49 o , how far is the top of the lamppost from the tip of its shadow? ANSWER 14. 6 ft