Question

solve each question below using the pythagorean theorem. round answers to the nearest hundredth. diagrams are not drawn to scale.

Explanation:

Step1: Recall Pythagorean Theorem

$a^{2}+b^{2}=c^{2}$ (c is hypotenuse).

Step2: For problem 1

$x=\sqrt{8^{2}-5^{2}}=\sqrt{64 - 25}=\sqrt{39}\approx6.24$ m.

Step3: For problem 2

$x=\sqrt{11^{2}-7^{2}}=\sqrt{121 - 49}=\sqrt{72}\approx8.49$ yd.

Step4: For problem 3

$x=\sqrt{6^{2}+8^{2}}=\sqrt{36 + 64}=\sqrt{100}=10$ in.

Step5: For problem 4

$x=\sqrt{15^{2}-10^{2}}=\sqrt{225 - 100}=\sqrt{125}\approx11.18$ cm.

Step6: For problem 5

$x=\sqrt{21^{2}-16^{2}}=\sqrt{441 - 256}=\sqrt{185}\approx13.60$ m.

Step7: For problem 6

$x=\sqrt{17^{2}-12^{2}}=\sqrt{289 - 144}=\sqrt{145}\approx12.04$ in.

Step8: For problem 7

$x=\sqrt{16^{2}+20^{2}}=\sqrt{256+400}=\sqrt{656}\approx25.61$ m.

Step9: For problem 8

$x=\sqrt{25^{2}-24^{2}}=\sqrt{625 - 576}=\sqrt{49}=7$ ft.

Step10: For problem 9

$x=\sqrt{12^{2}+5^{2}}=\sqrt{144 + 25}=\sqrt{169}=13$ in.

Answer:

1. 6.24 m
2. 8.49 yd
3. 10 in
4. 11.18 cm
5. 13.60 m
6. 12.04 in
7. 25.61 m
8. 7 ft
9. 13 in