Question

find the missing side length (include units). round to the nearest hundredth, if necessary. 14.7 yd 6.7 yd x find the missing side length (include units). round to the nearest hundredth, if necessary. 9.7 m 9.5 m x

Explanation:

Step1: Apply Pythagorean theorem for first triangle

For a right - triangle with sides \(a = 6.7\) yd, \(b = 14.7\) yd and hypotenuse \(x\), the Pythagorean theorem is \(x=\sqrt{a^{2}+b^{2}}\). So \(x=\sqrt{(6.7)^{2}+(14.7)^{2}}=\sqrt{44.89 + 216.09}=\sqrt{260.98}\approx16.15\) yd.

Step2: Apply Pythagorean theorem for second triangle

For a right - triangle with hypotenuse \(a = 9.7\) m and one side \(b = 9.5\) m and the other side \(x\), the Pythagorean theorem is \(x=\sqrt{a^{2}-b^{2}}\). So \(x=\sqrt{(9.7)^{2}-(9.5)^{2}}=\sqrt{(9.7 + 9.5)(9.7 - 9.5)}=\sqrt{(19.2)\times(0.2)}=\sqrt{3.84}\approx1.96\) m.

Answer:

16.15 yd, 1.96 m