Question

1. a = 3, b = 4, find c
2. a = 6, b = 12, find c
3. a = 8, b = 16, find c
4. a = 7, c = 25, find b
5. b = 9, c = 15, find a
6. a = 6, b = 8, find c
7. a = 9, b = 40, find c
8. a = 12, c = 13, find b
9. b = 24, c = 25, find a
10. a = 20, b = 21, find c
11. a = 5, c = 13, find b
12. b = 7, c = 25, find a
13. a = 9, b = 12, find c
14. a = 15, c = 17, find b

15 b = 9, c = 41, find a

Explanation:

Step1: Apply Pythagorean theorem

For right - triangle with sides \(a\), \(b\) and hypotenuse \(c\), \(c^{2}=a^{2}+b^{2}\) (when finding \(c\)) or \(b^{2}=c^{2}-a^{2}\) (when finding \(b\)) or \(a^{2}=c^{2}-b^{2}\) (when finding \(a\))

Step2: Calculate each value

1. \(c=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}=5\)
2. \(c=\sqrt{6^{2}+12^{2}}=\sqrt{36+144}=\sqrt{180}=6\sqrt{5}\)
3. \(c=\sqrt{8^{2}+16^{2}}=\sqrt{64 + 256}=\sqrt{320}=8\sqrt{5}\)
4. \(b=\sqrt{25^{2}-7^{2}}=\sqrt{625 - 49}=\sqrt{576}=24\)
5. \(a=\sqrt{15^{2}-9^{2}}=\sqrt{225-81}=\sqrt{144}=12\)
6. \(c=\sqrt{6^{2}+8^{2}}=\sqrt{36 + 64}=\sqrt{100}=10\)
7. \(c=\sqrt{9^{2}+40^{2}}=\sqrt{81+1600}=\sqrt{1681}=41\)
8. \(b=\sqrt{13^{2}-12^{2}}=\sqrt{169-144}=\sqrt{25}=5\)
9. \(a=\sqrt{25^{2}-24^{2}}=\sqrt{625-576}=\sqrt{49}=7\)
10. \(c=\sqrt{20^{2}+21^{2}}=\sqrt{400+441}=\sqrt{841}=29\)
11. \(b=\sqrt{13^{2}-5^{2}}=\sqrt{169 - 25}=\sqrt{144}=12\)
12. \(a=\sqrt{25^{2}-7^{2}}=\sqrt{625-49}=\sqrt{576}=24\)
13. \(c=\sqrt{9^{2}+12^{2}}=\sqrt{81+144}=\sqrt{225}=15\)
14. \(b=\sqrt{17^{2}-15^{2}}=\sqrt{289-225}=\sqrt{64}=8\)
15. \(a=\sqrt{41^{2}-9^{2}}=\sqrt{1681 - 81}=\sqrt{1600}=40\)

Answer:

1. \(5\)
2. \(6\sqrt{5}\)
3. \(8\sqrt{5}\)
4. \(24\)
5. \(12\)
6. \(10\)
7. \(41\)
8. \(5\)
9. \(7\)
10. \(29\)
11. \(12\)
12. \(24\)
13. \(15\)
14. \(8\)
15. \(40\)