WarmUp Exercises Use this diagram for Exercises 1

Warm-Up Exercises Use this diagram for Exercises 1– 4. 1. If PR = 12 and m ANSWER R = 19°, find p. 11. 3 2. If m P = 58° and r = 5, find p. ANSWER 8. 0

Warm-Up Exercises Use this diagram for Exercises 1– 4. 3. If m P = 60°, and p = 9 , find q. ANSWER 10. 4 4. If r = 8 and p = 12, find q. ANSWER 14. 4

Warm-Up Exercises Use this diagram for Exercises 1 - 4. 2. If a = 17 and m A = 31 o, find b to the nearest tenth. 1. If a = 18, b = 80 and c = 81, find tan B and tan A; sin B and sin A; cos B and cos A; Write each answer as a fraction and a decimal rounded to 4 places. 3. 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?

Answers Warm-Up Exercises ANSWER 1) tan B = 40 = 4. 4444; tan A = 9 = 0. 2250 40 9 ANSWER 1) sin B = 80 = 0. 9877; sin A = 2 = 0. 2222 9 81 ANSWER 1) cos B = 2 = 0. 2222; cos A = 80 = 0. 9877 81 9 ANSWER 2) 28. 3 ANSWER 3) 14. 6 ft

Trig Video

Lesson 7. 7 Using Inverse Trig Functions If you have the lengths of any two sides of a right triangle then you can find the acute angle measures using an inverse tangent, sine, or cosine funcgtion. tan-1 x is read as “the inverse tangent of x. ”

Use the calculator to find each angle measure to the nearest tenth of a degree 1. tan A = 2. 0035 1. m ﮮ A ≈ 63. 5˚ 2. cos B = 0. 7980 2. m ﮮ B ≈ 37. 1˚ 3. sin X = 23/40 3. m ﮮ X ≈ 35. 1˚ 4. tan C = 8/5 4. m ﮮ C ≈ 58. 0˚

Warm-Up 1 Exercises EXAMPLE Use an inverse tangent to find an angle measure Use a calculator to approximate the measure of the nearest tenth of a degree. A to SOLUTION 15 3 Because tan A = = = 0. 75, tan– 1 0. 75 = m 20 4 Use a calculator. tan – 1 0. 75 36. 86989765. . . ANSWER So, the measure of A is approximately 36. 9 o. A

Warm-Up Exercises GUIDED PRACTICE for Examples 1 1. Look back at Example 1. Use a calculator and an inverse tangent to approximate m C to the nearest tenth of a degree. ANSWER 53. 1 o

Warm-Up 2 Exercises EXAMPLE Solve a real-world problem THEATER DESIGN Suppose your school is building a raked stage. The stage will be 30 feet long from front to back, with a total rise of 2 feet. A rake (angle of elevation) of 5 o or less is generally preferred for the safety and comfort of the actors. Is the raked stage you are building within the range suggested?

Warm-Up 2 Exercises EXAMPLE Solve a real-world problem SOLUTION Use the sine and inverse sine ratios to find the degree measure x of the rake. sin xo = opp. = 2 hyp 30 x sin – 1 0. 0667 3. 842 ANSWER The rake is about 3. 8 o, so it is within the suggested range of 5 o or less.

Find angle measures and lengths of sides using trig ratios 1. b = ____ 9. 24 2. c = ____ 11. 02 c 33˚ 6 b B 12 3. m ﮮ A ≈ 36° C 7 A

Solve application problems using trig ratios 1. A flagpole 50 feet high stands on top of a building. From a point in front of a grocery store, the angle of elevation to the top of the pole is 58 degrees. How far is the grocery store from the base of the flag? 31. 25 feet 2. An airplane rises vertically 1000 feet over a horizontal distance of 1 mile. What is the angle of elevation of the airplane’s path? 11˚ 3. At a point on the ground 50 feet from the base of the tree, the angle of elevation is 53 degrees. Find the height of the tree. 66 feet

Application problems continued 4. A 50 meter vertical tower is braced with a cable secured at the top and tied 30 meters from the base. What angle does the cable 59˚ form with the ground? 5. A forest ranger spots a fire from the top of a lookout tower. The tower is 160 meters tall. The angle of depression is 12 degrees. How far is the fire from the tower? 753 feet

Application problems continued 6. The height of a flagpole is 12 meters. A student stands 50 meters from the base of the flagpole. What is the measure of the angle of elevation from the ground to the top of the flagpole? 13˚

Warm-Up Exercises Daily Homework Quiz Use this diagram for exercises 1 -3. 1. If x = 9 and z = 11 find m degree. X to the nearest tenth of a ANSWER 54. 9° 2. If y = 5 and z = 12 find m degree. ANSWER 63. 4° X to the nearest tenth of a

Warm-Up Exercises Daily Homework Quiz Use this diagram for exercises 1 -3. If m Y = 17. 4° and z = 12 solve ∆XYZ. ANSWER The angles are 17. 4°, 72. 6°, and 90°; the sides are 12, about 3. 6, and about 11. 5.