Right triangles day2
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1. The document discusses trigonometric ratios and how to use them to solve for missing side lengths and angle measures in right triangles. 2. It provides examples of setting up trig ratios, using the Pythagorean theorem, and using inverse trig functions to find missing angles. 3. The key steps are to label the sides of the right triangle, set up the appropriate trig ratios based on which information is known or missing, and use trig identities or the inverse functions to calculate the missing information.
Right triangles day2
- 1. I can label the sides of a right triangle. I can set up the trig ratios. I can use the trig ratios to solve for the missing side length & angle measures of a right triangle.
- 2. H AT 15 9 Calculate the length of hypotenuse leg leg ? Use the Pythagorean theorem -81 -81 x = 12
- 3. H AT 15 9 hypotenuse Opp. leg Adj. leg 12 Set up the following trig ratios Sin H = Cos H = Tan H = Sin A = Cos A = Tan A = Adj. leg Opp. leg
- 4. H C Calculate the length of hypotenuse legleg ? Use the Pythagorean theorem x = 6
- 5. hypotenuse Set up the following trig ratios H C 6 Sin S = Cos S = Tan S = Sin H = Cos H = Tan H = Adj. leg Opp. leg
- 6. If Sin A = , find the Cos A. *Draw a triangle and label. A Opp.leg Adj. leg 6 8 x -36 -36 Cos A =
- 7. Use the last example as a model problem to complete the following: 1. If Tan A = , find Sin B. 2. If Cos B = , find Tan A.
- 8. Solving Right Triangles means to calculate missing side lengths and angle measures of a right triangle. When evaluating sine, cosine, or tangent you need to make sure your calculator is in degree mode. MODE Radian Degree
- 9. Evaluating Angles in the calculator. (A) Sin 52 o (B) Cos 122 o (C) Tan 45 o (D) Sin 0 o (E) Cos 90 o (F)Tan 90 o
- 10. A B C x y 250 37 o Solve for x and y Why can’t you use the Pythagorean Theorem?Opp. leg Adj. leg Which side should be the longest? Why?
- 11. Solve for x and y A B C x y 10 61 o Opp. leg Adj. leg
- 12. Solve for x and y A B C x 13 34 o Opp. leg Adj. leg
- 13. Using the inverse function to solve for angles Notice if you use the 2nd button and then choose a trig function, you are using the inverse. Sin-1 Cos-1 Tan-1 (a) (b)Sin-1 Sin-1 Cos-1 Cos-1
- 14. Use the examples on the previous slide as model problems to help complete the following problems. (c) (d) (e) (f) Sin-1 Sin-1
- 15. Find the measures of the acute angles in a right triangle. *Remember: the 2 acute angles of a right triangle are complementary FIND: m<A and m<B A B C 11.2 Opp. leg Adj. leg 9.8 + 80.2 = 90
- 16. A BC 10.8 24.7 Find the m<A and m<B
- 17. A BC 72 Find the m<A and m<B