Question

part 1 - pythagorean theorem

1. a right triangle has legs of 3 and 4. find the hypotenuse.
2. a right triangle has one leg of 5 and a hypotenuse of 13. find the missing leg.
3. a right triangle has legs of 9 and 12. find the hypotenuse.
4. a right triangle has one leg of 8 and a hypotenuse of 17. find the missing leg.

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\).

Step2: Solve problem 1

Let \(a = 3\) and \(b = 4\). Then \(c=\sqrt{a^{2}+b^{2}}=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}=5\).

Step3: Solve problem 2

Let \(a = 5\) and \(c = 13\). Then \(b=\sqrt{c^{2}-a^{2}}=\sqrt{13^{2}-5^{2}}=\sqrt{169 - 25}=\sqrt{144}=12\).

Step4: Solve problem 3

Let \(a = 9\) and \(b = 12\). Then \(c=\sqrt{a^{2}+b^{2}}=\sqrt{9^{2}+12^{2}}=\sqrt{81+144}=\sqrt{225}=15\).

Step5: Solve problem 4

Let \(a = 8\) and \(c = 17\). Then \(b=\sqrt{c^{2}-a^{2}}=\sqrt{17^{2}-8^{2}}=\sqrt{289 - 64}=\sqrt{225}=15\).

Answer:

1. 5
2. 12
3. 15
4. 15