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## 9.1 – 9.3 Solving Right Triangles without Trigonometry

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**x**15 8 10 2. Find the length of the altitude drawn to the hypotenuse. • x = 10.95 • x = 11.5 • x = 13.56 • None of the above <Explanation follows.>**8**x 23 15 x x 15 x x 8 15 8 A A C B C C D B D 2. Solution You can redraw the triangles: So, x2 = 8*15 x2 = 120 x = 10.95 (A)**9**3. Find the value of x. • x = 219 • x = 437 • x = 223 • x = 23 x 19 4 <Explanation follows.>**19**x x 23 A A C B C C D B D 3. Solution You can redraw the triangles: x 19 4 x 23 19 x So, x2 = 19*23 x2 = 437 x = 437 4 19**10**4. The geometric mean of 5 and 15 is: • 3 • 10 • 5 3 • 75 <Explanation follows.>**5**x x 15 4. Solution Geometric mean: So, x2 = 75 x = 75 x = 253 x = 53**9**9. Find the value of x. • 8.3 • 7.0 • 10.1 • 1.9**7**10. Choose the sets that are possible side lengths of a right triangle. • 1,1,2 • 1,1,2 • 3,4,7 • 3,4,5 • a and c • b and d**10**9 10.A. Find the side length of a square with a diagonal of length 10. • 3 • 4.5 • 7.07 • 9 <Explanation follows.>**10**10.A. Solution x x So, x2 + x2= 100 2x2 = 100 x2 = 50 x = 7.07**11.6**6 h 10 9 15. Find the value of h. • h = 3.5 • h = 5.1 • h = 7.5 • h = 10.77 <Explanation follows.>**11.6**11.6 6 10 6 10 11.6 h h 6 h 10 A A C B C C D B D 15. Solution You can redraw the triangles: 10 11.6 10 6 h h 6**10**11. Which statements are true about options B and C in #11? • B is acute and C is obtuse • B is obtuse and C is acute • B is acute and C is not a triangle • B is obtuse and C is not a triangle <Explanation follows.>**11. Solution**• 6,7,12 • 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. 122 _____ 62 + 72 • ______ 36 + 49 • C. 74.2______20.8 + 39**9**13. Find the value of x. • x = 257 • x = 133 • x = 19 • x = 221 x 12 7