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Warm Up for Section 1.3 (1). In a 30 o -60 o -90 o triangle, the hypotenuse

Warm Up for Section 1.3 (1). In a 30 o -60 o -90 o triangle, the hypotenuse measures 8 inches. What is the length of the short leg? (2). In a 45 o -45 o -90 o triangle, the hypotenuse measures 12 inches. What is the length of one leg?

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Warm Up for Section 1.3 (1). In a 30 o -60 o -90 o triangle, the hypotenuse

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  1. Warm Up for Section 1.3 (1). In a 30o-60o-90o triangle, the hypotenuse measures 8 inches. What is the length of the short leg? (2). In a 45o-45o-90o triangle, the hypotenuse measures 12 inches. What is the length of one leg? (3). In a 30o-60o-90o triangle, the long leg measures 7inches. What is the length of the hypotenuse? (4). cos T = (5). tan R = R s t S T r

  2. Answers for Warm Up Section 1.3 (1). In a 30o-60o-90o triangle, the hypotenuse measures 8 inches. What is the length of the short leg? (2). In a 45o-45o-90o triangle, the hypotenuse measures 12 inches. What is the length of one leg? (3). In a 30o-60o-90o triangle, the long leg measures 7 inches. What is the length of the hypotenuse? (4). cos T = (5). tan R = R s t S T r

  3. Work for Answers to WU, Section 1.3 (1). (2). (3). 30o 60o 30o 45o 60o 45o

  4. Homework Answers for Section 1.2 • Trig Ratios • sin A: sin B: • cos A: cos B: • tan A: tan B: 2. sin A: sin B: cos A: cos B: tan A: tan B: 3. sin A: sin B: cos A: cos B: tan A: tan B: 4. sin A: sin B: cos A: cos B: tan A: tan B:

  5. Homework Answers for Section 1.2 6. x ≈38.6 y ≈37.3 5. x ≈ 11.3 y ≈4.1 7. x ≈9.1 y ≈4.3 8. x ≈21.9 y ≈11.0 10. x ≈8.6 y ≈12.3 9. x ≈19.1 y ≈19.1

  6. Trigonometric Ratios: Missing Angle Section 1.3 Standard: MCC9-12.G.SRT.7 Essential Question: How can trig ratios be used to find angle measures?

  7. Vocabulary: Adjacent Leg: The leg next to the reference angle in a right triangle. Opposite Leg: The leg across from the reference angle in a right triangle. Trigonometric ratio:  A ratio that describes a relationship between the sides and angles of a triangle. Sine: In a right triangle, the ratio of the length of the leg opposite the angle divided by the hypotenuse.

  8. Cosine: In a right triangle, the ratio of the length of the leg adjacent to the angle divided by the hypotenuse. Tangent: In a right triangle, the ratio of the length of the leg opposite the angle divided by the length of the adjacent leg. Similar Triangles: triangles with corresponding angles are congruent and corresponding sides are proportional

  9. Remember from yesterday, the following ratios: ___ ___ ___ ___ ___ ___ ___ ___ ___ S O H C A H T O A Find x. 31˚ 5 x

  10. Remember from yesterday, the following ratios: ___ ___ ___ ___ ___ ___ ___ ___ ___ S O H C A H T O A Find x. x˚ 12 5

  11. To find a missing angle when given at least two sides, we will have to use the inverse trig ratios. The inverse trigonometric feature on a calculator will allow you to go backwards! If you know the trigonometric ratio, the calculator can provide the measure of an acute angle in the right triangle.

  12. Example: Compute the value of using your calculator. Step 1: Set your calculator to degree mode. Step 2: Press then ENTER. Step 3: The value on the screen is the measure of the reference angle. So,  34.8o or 35o. 2nd sin 4 ÷ 7 )

  13. Find x. (1). (2). (3). x° 23 2 x° 16 14 xo 10

  14. Try these with your partner: Find x. (4). (5). (6). 12 74 11 13 32 42° x° x x°

  15. (7). (8). (9). 14 x x x° 20 63° 17 50 59°

  16. (10). A 20-foot ladder is leaning against a wall. The base of the ladder is 3 feet from the wall. What angle does the ladder make with the ground? 20 x° 3

  17. 22 53 x° STICKY PROBLEM Set up and solve a trigonometric equation to find the value of x. Show all work. Round each edge to the nearest tenth and each angle to the nearest degree.

  18. 37 21° x STICKY PROBLEM Set up and solve a trigonometric equation to find the value of x. Show all work. Round each edge to the nearest tenth and each angle to the nearest degree.

  19. 29 x° 5 STICKY PROBLEM Set up and solve a trigonometric equation to find the value of x. Show all work. Round each edge to the nearest tenth and each angle to the nearest degree.

  20. x 12 42° STICKY PROBLEM Set up and solve a trigonometric equation to find the value of x. Show all work. Round each edge to the nearest tenth and each angle to the nearest degree.

  21. 23 x° 16 STICKY PROBLEM Set up and solve a trigonometric equation to find the value of x. Show all work. Round each edge to the nearest tenth and each angle to the nearest degree.

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