2. Using trig ratios in equations Remember back in 1 st grade when you had to solve: 12 = x What did you do? 6 (6) 72 = x Remember back in 3rd grade when x was in the denominator? 12 = 6 What did you do? x (x) 12x = 6 __ 12 x = 1/2

3. There are 3 kinds of trigonometric ratios we learned. sine ratio cosine ratio tangent ratio Three Types Trigonometric Ratios

4. Trigonometric Ratios  When do we use them? – On right triangles that are NOT 45-45-90 or 30-60- 90 Find: tan 45 1 Why? tan = opp adj

5. If using a calculator… I want to find…Use these calculator keys Side length measure SIN COS TAN Angle measure SIN -1 COS -1 TAN -1

6. 42 cm 22 cm θ This time, you’re looking for theta. Ask yourself: In relation to the angle, what pieces do I have? Opposite and hypotenuse Ask yourself: What trig ratio uses opposite and hypotenuse? sine Set up the equation (remember you’re looking for theta): Sin θ = 22 42 Remember to use the inverse function when you find theta THIS IS IMPORTANT!! Sin -1 22 = θ 42 31.59°= θ

7. 17 cm 22 cm θ You’re still looking for theta. Ask yourself: What trig ratio uses the parts I was given? tangent Set it up, solve it, tell me what you get. tan θ = 17 22 THIS IS IMPORTANT!! tan -1 17 = θ 22 37.69°= θ

8. Your turn: 4 7 In the figure, find sin  Sin  = Opposite Side hypotenuse = 4 7  = 34.85 

9.  Solve the right triangle. Round the decimals to the nearest tenth.

10.  Solve the right triangle. Round decimals to the nearest tenth. 25 ° You are looking for opposite and hypotenuse which is the sin ratio. sin H = opp. hyp. 13 sin 25 ° = h 13 13(0.4226) ≈ h 5.5 ≈ h Set up the correct ratio Substitute values/multiply by reciprocal Substitute value from table or calculator Use your calculator to approximate.

11.  How do we use right triangles to solve real life problems?

12. Indirect Measurement Find the height of the tree given an angle and the length of the shadow of the tree.

13. Using Right Triangles in Real Life  Space Shuttle: During its approach to Earth, the space shuttle’s glide angle changes.  When the shuttle’s altitude is about 15.7 miles, its horizontal distance to the runway is about 59 miles. What is its glide angle? Round your answer to the nearest tenth.

14. Solution:  You know opposite and adjacent sides. If you take the opposite and divide it by the adjacent side, then take the inverse tangent of the ratio, this will give you the slide angle. tan x ° = opp. adj. tan x ° = 15.7 59 ≈ 14.9 Use correct ratio Substitute values  When the space shuttle’s altitude is about 15.7 miles, the glide angle is about 14.9 °. 15.7 miles 59 miles x°x°

15.  When the space shuttle is 5 miles from the runway, its glide angle is about 19°. Find the shuttle’s altitude at this point in its descent. Round your answer to the nearest tenth. 19 ° 5 miles h tan 19 ° = opp. adj. tan 19 ° = h 5 Use correct ratio Substitute values 5 tan 19 ° = h 5 5 Isolate h by multiplying by 5. 1.7 ≈ h Approximate using calculator

16. Conclusion Make Sure that the triangle is right-angled