Question

1. determine the missing side lengths. show your calculations and round to the nearest tenth if needed.

a)
b)

Explanation:

Step1: Apply Pythagorean theorem for part a)

For a right - triangle with legs \(a = 3\) in and \(b=14\) in, and hypotenuse \(x\). The Pythagorean theorem is \(a^{2}+b^{2}=x^{2}\).
Substitute \(a = 3\) and \(b = 14\) into the formula: \(x^{2}=3^{2}+14^{2}=9 + 196=205\).
Then \(x=\sqrt{205}\approx14.3\) in.

Step2: Apply Pythagorean theorem for part b)

For a right - triangle with one leg \(a = 8\) ft, hypotenuse \(c = 10\) ft, and the other leg \(x\). Using the Pythagorean theorem \(a^{2}+x^{2}=c^{2}\), we can solve for \(x\).
Rearrange the formula to \(x^{2}=c^{2}-a^{2}\). Substitute \(a = 8\) and \(c = 10\): \(x^{2}=10^{2}-8^{2}=100 - 64 = 36\).
Then \(x=\sqrt{36}=6\) ft.

Answer:

a) \(x\approx14.3\) in
b) \(x = 6\) ft