Unit 8: Right Triangle Trigonometry

1. Unit 8: Right Triangle Trigonometry TEST 4/04 Define trigonometric ratios and solve problems involving right triangles

2. Ratios in Right Triangles WHAT YOU WILL LEARN • To find trigonometric ratios using right triangles, and • To solve problems using trigonometric ratios.

3. Trigonometric Ratios A RATIO is a comparison of two numbers. In Trigonometry, the comparison is between sides of a triangle.

4. DEFINITIONS • Trigonometry: The study of the properties of triangles and trigonometric functions and their applications. “Triangle Measurement” • Trigonometric ratio: A ratio of the measures of two sides of a right triangle is called a trigonometric ratio.

5. Trigonometric Ratios • When do we use them? • On right triangles that we are solving for missing sides or angles.

6. Side Opposite q Side Adjacent q Naming Sides of Right Triangles Hypotenuse q

7. Side Opposite q Side Adjacent q Hypotenuse We will look at each of these trig functions from the right triangle perspective.

8. Trig. Ratios

9. Three Trigonometric Ratios • Sine – abbreviated ‘sin’. • Ratio: sin θ = opposite side hypotenuse • Cosine - abbreviated ‘cos’. • Ratio: cos θ = adjacent side hypotenuse • Tangent - abbreviated ‘tan’. • Ratio: tan θ = opposite side adjacent side Θ this is the symbol for an unknown angle measure. It’s name is ‘Theta’. Easy way to remember trig ratios: SOH CAH TOA

10. Great Chief Soh Cah Toa A young brave Native American boy, frustrated by his inability to understand the geometric constructions of his tribe's battle dress, angrily kicked a stone and crushed his big toe. Fortunately, he learned from this experience, and began to use his noodle to solve his problems rather than violence. This was especially useful in his Math class, and he went on to become the smartest man of his tribe. He studied many concepts in math, especially trigonometry; and even today we remember many of the functions by his name. When he grew up, the tribal priest gave him a name that reflected his special talents - one that reminded the tribe of his great discoveries. But, because he was troubled throughout his life by the problematic big toe, he was constantly at the edge of the river, soaking the toe in the cooling waters. For that behavior, he was named Chief SohCah Toa.

11. a2 + b2 = c2 42 + 32 = c2 16 + 9 = c2 25 = c2  5 Example 1:Find the exact value of the six trig functions using the triangle given. 4 3 sin  = opp/hyp = 3/5 cos  = adj/hyp = 4/5 tan  = opp/adj = 3/4

12. a2 + b2 = c2 12 + b2 = 22 1 + b2 = 4 b2 = 3 3 Example 2:Find the exact value of the three trig functions using the triangle given. 2 1  sin  = opp/hyp = cos  = adj/hyp = 1/2 tan  = opp/adj =

13. Calculator Buttons Find each value using a calculator. Round to the nearest ten thousandths. • Cos 41 • Sin 78 • Tan 82

14. 20 m x Find x. Round to the nearest tenth. adj opp

15. 283 m x Find the missing side. Round to the nearest tenth. hyp opp

16. Find the missing side. Round to the nearest tenth. hyp 20 ft x adj