Question

calculator
what is the value of x?
round to the nearest tenth, if necessary.
x = 6
x = 11
x = 11.5
x = 13.6
triangle with right angle at b, vertices a (top), b (bottom left), c (bottom right); ab = x, bc = 8, ac = 14

Explanation:

Step1: Identify the triangle type

The triangle \(ABC\) is a right - triangle with right angle at \(B\), hypotenuse \(AC = 14\) and one leg \(BC=8\), and the other leg \(AB = x\). We can use the Pythagorean theorem which states that for a right - triangle with legs \(a\), \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). In this case, \(x^{2}+8^{2}=14^{2}\).

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

First, calculate \(8^{2}=64\) and \(14^{2} = 196\). Then, rewrite the equation as \(x^{2}=14^{2}-8^{2}\). Substitute the values: \(x^{2}=196 - 64\). So, \(x^{2}=132\).

Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{132}\). Calculate \(\sqrt{132}\approx11.5\) (rounded to the nearest tenth).

Answer:

\(x = 11.5\) (corresponding to the option \(x = 11.5\))