Question

find the value of x.
triangle with right angle, side x, side 7, base 14
x = ?
round to the nearest tenth.

Explanation:

Step1: Identify the triangle type

This is a right - triangle, so we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - triangle with hypotenuse \(c\) and legs \(a\) and \(b\), \(a^{2}+b^{2}=c^{2}\). In this triangle, the hypotenuse \(c = 14\), one leg \(b = 7\), and the other leg is \(x\). So the formula becomes \(x^{2}+7^{2}=14^{2}\).

Step2: Solve for \(x^{2}\)

First, calculate \(7^{2}=49\) and \(14^{2}=196\). Then, we can rewrite the equation as \(x^{2}=14^{2}-7^{2}\). Substituting the values, we get \(x^{2}=196 - 49=147\).

Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{147}\). We know that \(\sqrt{147}=\sqrt{49\times3}=7\sqrt{3}\approx7\times1.732 = 12.124\). Rounding to the nearest tenth, we look at the hundredth place. The number is \(12.124\), and the digit in the hundredth place is \(2\), which is less than \(5\), so we round down. So \(x\approx12.1\).

Answer:

\(12.1\)