Question

pythagorean theorem assignment
solve for missing side lengths: state whether each problem has a missing hypotenuse (c) or missing leg (a) then solve. points will be deducted if work is not shown.

1. x =

missing side: hypotenuse

1. x =

missing side: hypotenuse

1. x =

missing side: leg

1. x =

missing side: leg

1. x =

missing side: hypotenuse

1. x =

missing side: leg

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). If we are finding a leg, say \(a\), then \(a=\sqrt{c^{2}-b^{2}}\); if finding the hypotenuse \(c\), then \(c = \sqrt{a^{2}+b^{2}}\).

Step2: Solve problem 1

Given legs \(a = 8\) and \(b = 15\). Using \(c=\sqrt{a^{2}+b^{2}}\), we have \(c=\sqrt{8^{2}+15^{2}}=\sqrt{64 + 225}=\sqrt{289}=17\).

Step3: Solve problem 2

Given hypotenuse \(c = 15\) and leg \(b = 12\). Using \(a=\sqrt{c^{2}-b^{2}}\), we have \(a=\sqrt{15^{2}-12^{2}}=\sqrt{225 - 144}=\sqrt{81}=9\).

Step4: Solve problem 3

Given legs \(a = 17\) and \(b = 5\). Using \(c=\sqrt{a^{2}+b^{2}}\), we have \(c=\sqrt{17^{2}+5^{2}}=\sqrt{289+25}=\sqrt{314}\approx17.7\).

Step5: Solve problem 4

Given legs \(a = 5\) and \(b = 10\). Using \(c=\sqrt{a^{2}+b^{2}}\), we have \(c=\sqrt{5^{2}+10^{2}}=\sqrt{25 + 100}=\sqrt{125}\approx11.2\).

Step6: Solve problem 5

Given hypotenuse \(c = 15\) and leg \(a = 12\). Using \(b=\sqrt{c^{2}-a^{2}}\), we have \(b=\sqrt{15^{2}-12^{2}}=\sqrt{225 - 144}=\sqrt{81}=9\).

Step7: Solve problem 6

Given hypotenuse \(c = 13\) and leg \(b = 12\). Using \(a=\sqrt{c^{2}-b^{2}}\), we have \(a=\sqrt{13^{2}-12^{2}}=\sqrt{169 - 144}=\sqrt{25}=5\).

Answer:

1. \(x = 17\)
2. \(x = 9\)
3. \(x\approx17.7\)
4. \(x\approx11.2\)
5. \(x = 9\)
6. \(x = 5\)