Question

directions: find the missing side lengths. show all work. round to the nearest ten
8.
9.
13
9
1
rror analysis:
26
10
$c^2 = a^2 + b^2$
$x^2 = 10^2 + 26^2$

Explanation:

Step1: Identify the triangle type

This is a right - triangle, so we can use the Pythagorean theorem \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs of the right - triangle. In the given triangle, the two legs are \(a = 10\) and \(b=13\), and we need to find the hypotenuse \(c\) (let's call it \(x\)).

Step2: Apply the Pythagorean theorem

Substitute \(a = 10\) and \(b = 13\) into the formula \(x^{2}=a^{2}+b^{2}\). So \(x^{2}=10^{2}+13^{2}\). Calculate \(10^{2}=100\) and \(13^{2}=169\). Then \(x^{2}=100 + 169=269\).

Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{269}\approx16.4\) (rounded to the nearest tenth).

Answer:

The length of the missing side is approximately \(16.4\)