Question

directions: find the missing side lengths. show all work. round to the nearest 8. 9. 10. error analysis: a) describe the error in using the pythagorean theorem.

Explanation:

Step1: Recall Pythagorean Theorem

The Pythagorean Theorem states that for a right - triangle with legs of lengths \(a\) and \(b\) and hypotenuse of length \(c\), \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse (the side opposite the right angle and the longest side of the right - triangle).

Step2: Analyze the given triangle

In the given right - triangle, the sides are \(x\) (one leg), \(10\) (one leg), and \(26\) (the hypotenuse). The hypotenuse \(c = 26\), and the legs are \(a=x\) and \(b = 10\). But in the calculation \(x^{2}=10^{2}+26^{2}\), the formula was misapplied. The correct formula should be \(c^{2}=a^{2}+b^{2}\), so \(26^{2}=x^{2}+10^{2}\), not \(x^{2}=10^{2}+26^{2}\). The error is that the hypotenuse was treated as a leg in the Pythagorean Theorem formula. The hypotenuse is the longest side, so it should be on the left - hand side of the equation \(c^{2}=a^{2}+b^{2}\), and the legs should be on the right - hand side.

Answer:

The error is that the hypotenuse (length 26) was incorrectly used as a leg in the Pythagorean Theorem. The correct formula for a right - triangle with legs \(x\) and \(10\) and hypotenuse \(26\) is \(26^{2}=x^{2}+10^{2}\), not \(x^{2}=10^{2}+26^{2}\).