1. The midpoint of is M(-4,6). If point R is (6, -9), find point J.

2. Determine whether the points (3, 4), (5, 1), and (2, -1) are vertices of a right triangle. (3,4) (5,1) (2, - 1) Yes

3. Trigonometric Functions with Right Triangles  Trig functions will be done involving a right triangle.  Trig functions are always done using one of the non-right angles  We set up ratios using the 3 sides of the triangle and solve for missing parts A BC

4. Trigonometric Functions with Right Triangles hypotenuse  The sides have names that we need to know to set up the ratios  The hypotenuse is always across from the right angle (we should already know this) A BC

5. Trigonometric Functions with Right Triangles hypotenuse  The other 2 sides names depend on which angle we are working with  For this problem we will say we are working with angle C A BC  Once we have established this – we can label the other 2 sides

6. Trigonometric Functions with Right Triangles hypotenuse  The opposite side is across (or opposite) the angle that we are working with  The remaining side is called the adjacent side A BC opposite adjacent

7. Trigonometric Functions with Right Triangles hypotenuse  There are 3 trig functions we will work with – sine (sin), cosine (cos), and tangent (tan) A BC opposite adjacent

8. Setting up the trig functions with numbers 5  The sides still have the same names – we just need to plug the numbers in A BC 3 4 hypotenuse opposite adjacent Find the sin C, cos C, tan C

9. Setting up the trig functions with numbers 5  The only difference is the angle we are working with is now A – the sides change A BC 3 4 hypotenuse opposite adjacent Find the sin A, cos A, tan A

10. Trigonometric Functions with Right Triangles  The calculator has a sin, cos, and tan button on it.  Make sure your calculator is in degree mode before using it A BC  You can use this button to find the value of an angle to help you solve for missing sides

11. Trigonometric Functions with Right Triangles  Set up the ratio using the information you have (4 is the opposite side and x is the adjacent – so use tangent) A BC Find side AB in the following triangle (round to the nearest tenth) 25º 9 x  In your calculator get the value for tan 25 (4 decimals)  Cross multiply and solve

12. Trigonometric Functions with Right Triangles A BC Find the missing sides 60º 9 x y opp hyp adj

13. Trigonometric Functions with Right Triangles A BC 35º 210 x opp hyp adj You are a crane operator with a 210 foot boom. You lift up a rock so that it is directly in front of you. The boom is at an angle of 35º. How far in front of you is the rock?