Question

1. use the pythagorean theorem to find x. round to the nearest tenth.

a.) (6)^2+(8)^2=x^2
36 + 64 = x^2
b.)

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 for part a

In the first right - triangle, \(a = 6\), \(b = 8\), and \(c=x\). By the Pythagorean Theorem, \(x^{2}=6^{2}+8^{2}\). Calculate \(6^{2}=36\) and \(8^{2}=64\), so \(x^{2}=36 + 64=100\). Then \(x=\sqrt{100}=10\).

Step3: Solve for part b

In the second right - triangle, \(a = 3\), \(c = 5\), and \(b=x\). Using the Pythagorean Theorem \(c^{2}=a^{2}+b^{2}\), we can rewrite it as \(b^{2}=c^{2}-a^{2}\). So \(x^{2}=5^{2}-3^{2}\), \(5^{2}=25\), \(3^{2}=9\), then \(x^{2}=25 - 9 = 16\), and \(x=\sqrt{16}=4\).

Answer:

a. 10
b. 4