Question

use the pythagorean theorem to find the missing side.
round to the nearest hundredth.
1
$a=$
$b = 33$
$c = 65$
2
$a = 6$
$b = 11$
$c=$
3
$a = 1$
$b = 3$
$c=$
4
$a = 6$
$b = 14$
$c=$

Explanation:

Step1: Recall the Pythagorean Theorem

The Pythagorean Theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse of a right - triangle and \(a\) and \(b\) are the other two sides. If one of the non - hypotenuse sides is missing, we can rewrite the formula as \(a=\sqrt{c^{2}-b^{2}}\) or \(b=\sqrt{c^{2}-a^{2}}\). If the hypotenuse \(c\) is missing, then \(c = \sqrt{a^{2}+b^{2}}\).

Problem 1:

Given \(b = 33\), \(c=65\), find \(a\).

Step2: Substitute into the formula \(a=\sqrt{c^{2}-b^{2}}\)

$$
LATEXBLOCK0
$$

Problem 2:

Given \(a = 6\), \(b = 11\), find \(c\).

Step2: Substitute into the formula \(c=\sqrt{a^{2}+b^{2}}\)

$$
LATEXBLOCK1
$$

Problem 3:

Given \(a = 1\), \(b = 3\), find \(c\).

Step2: Substitute into the formula \(c=\sqrt{a^{2}+b^{2}}\)

$$
LATEXBLOCK2
$$

Problem 4:

Given \(a = 6\), \(b = 14\), find \(c\).

Step2: Substitute into the formula \(c=\sqrt{a^{2}+b^{2}}\)

$$
LATEXBLOCK3
$$

Answer:

1. \(a = 56\)
2. \(c\approx12.53\)
3. \(c\approx3.16\)
4. \(c\approx15.23\)