Question

1. describe and correct the error.

(there is a right triangle with hypotenuse 26, one leg 10, and the other leg x. the following calculation is shown:
$c^2 = a^2 + b^2$
$x^2 = 10^2 + 26^2$
$x^2 = 100 + 676$
$x^2 = 776$
$x = \sqrt{776}$
$x \approx 27.9$)

Explanation:

Step1: Identify Hypotenuse Error

In a right triangle, \( c \) (hypotenuse) is the longest side. Here, hypotenuse is \( 26 \), but \( 26 < 27.9 \) (incorrect \( x \)), so \( x \) is not hypotenuse. Correctly, hypotenuse is \( 26 \), so formula should be \( 26^2 = 10^2 + x^2 \).

Step2: Rearrange Formula

Rearrange \( c^2 = a^2 + b^2 \) to \( x^2 = c^2 - a^2 \). Substitute \( c = 26 \), \( a = 10 \): \( x^2 = 26^2 - 10^2 \).

Step3: Calculate Squares

\( 26^2 = 676 \), \( 10^2 = 100 \). So \( x^2 = 676 - 100 = 576 \).

Step4: Take Square Root

\( x = \sqrt{576} = 24 \).

Answer:

The error was misidentifying the hypotenuse (used \( x \) as a leg but treated it as a non - hypotenuse, then incorrectly applied Pythagorean theorem). Correct solution: \( x = 24 \) (steps: \( 26^2 = 10^2 + x^2 \Rightarrow x^2 = 676 - 100 = 576 \Rightarrow x = \sqrt{576}=24 \)).