9.1 – 9.3 Solving Right Triangles without Trigonometry

2. Find the length of the altitude drawn to the hypotenuse x a)x = b)x = 11.5 c)x = d)None of the above

2. Solution 15 8 x You can redraw the triangles: B A CD C B D A C 8 x x x x 8 So, x 2 = 8*15 x 2 = 120 x = (A)

3. Find the value of x x a)x = 2  19 b)x =  437 c)x = 2  23 d)x =  23

3. Solution You can redraw the triangles: B A CD C B D A C 4 x x1923 x x 19 So, x 2 = 19*23 x 2 = 437 x =  x

4. The geometric mean of 5 and 15 is: a)3 b)10 c)5  3 d)75

4. Solution Geometric mean: 15 x x 5 So, x 2 = 75 x =  75 x =  25  3 x = 5  3

9. Find the value of x. a)8.3 b)7.0 c)10.1 d)1.9

10. Choose the sets that are possible side lengths of a right triangle. a)1,1,2 b)1,1,  2 c)3,4,7 d)3,4,5 e)a and c f)b and d

10.A. Find the side length of a square with a diagonal of length a)3 b)4.5 c)7.07 d)9

10.A. Solution So, x 2 + x 2 = 100 2x 2 = 100 x 2 = 50 x = x x

15. Find the value of h h 11.6 a)h = 3.5 b)h = 5.1 c)h = 7.5 d)h = 10.77

15. Solution You can redraw the triangles: B A CD C B D A C h 10 h 11.6 h h h

11. Which statements are true about options B and C in #11? a)B is acute and C is obtuse b)B is obtuse and C is acute c)B is acute and C is not a triangle d)B is obtuse and C is not a triangle

11. Solution B.6,7,12 C.20.8, 39, 74.2 Put the largest first and confirm it can be a triangle. If yes, square them and compare largest to other two: B _____ ______ C. 74.2______

13. Find the value of x x a)x = 2  57 b)x =  133 c)x =  19 d)x = 2  21