1. Geometry Section 9.5 Trigonometric ratios

2. The word “trigonometry” comes from two Greek words which mean ___________________ And that is exactly what we will do with trigonometry - we will find the measures of angles and the length of sides in triangles. While trigonometry can be applied to any type of triangle, we will limit ourselves to right triangles. triangle measurement

3. A trigonometric ratio (i.e. fraction) is a ratio of the lengths of two sides of a right triangle. The three basic trigonometric ratios are sine (___), cosine (___) and tangent (___). These ratios are defined for the acute angles of a right triangle as follows.

4. sin A = -------------- cos A = -------------- tan A = ------------- opposite leg hypotenuse adjacent leg hypotenuse opposite leg adjacent leg If we write the ratios for the acute angle B instead, then the opposite leg and adjacent leg would be switched!!!!

5. An easy way to remember these three trig ratios is with the mnemonic SOH-CAH-TOA ININ PPPP YPYP OSOS DJDJ YPYP ANAN PPPP DJDJ

6. Example: Write the correct ratio for each trigonometric ratio. 3535 4545 3434

7. Example: Write the correct ratio for each trigonometric ratio. Sin O = Cos G = Tan G =

8. The value of the sine, cosine and tangent of an angle depend only upon the measure of the angle and not the size of the triangle that the angle is found in.

9. A scientific calculator can be used to find the value of these three trig ratios. Make sure your calculator is in degree mode. sin 13 0 = ___________ cos 77 0 = ____________ tan 40 0 = ____________

10. We can use the trig ratios to find the lengths of unknown sides in right triangles.

11. Example: Solve for x and y. Round your answers to the nearest 1000 th.

13. Example: The angle of elevation to the top of a tree from a point 100 feet from the base of the tree is 51 0. Estimate the height of the tree to the nearest 1000 th. NOTE: the angle of elevation is the angle formed by a horizontal line (usually the ground) and the line of sight up to some object.

14. Example: The angle of elevation to the top of a tree from a point 100 feet from the base of the tree is 51 0. Estimate the height of the tree to the nearest 1000 th.

15. Example: A support wire for a tall radio tower is 280 ft. long and is attached to the tower at a point exactly half way up the tower. If the wire makes an angle of 64 o with the ground, find the height of the tower to the nearest 1000 th of a foot.