Question

1. consider the diagram. find the values of x and y. if your answer cannot be expressed as a rational number, use square root notation to write the value. the value of x is ______. the value of y is ______.

Explanation:

Step1: Use Pythagorean theorem for x

In the right - triangle with legs 5 and 8, by the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 5\), \(b = 8\) and \(c=x\). So \(x=\sqrt{5^{2}+8^{2}}\).
\[x=\sqrt{25 + 64}=\sqrt{89}\]

Step2: Use Pythagorean theorem for y

The base of the large right - triangle is \(4 + 8=12\) and the height is 5. By the Pythagorean theorem, \(y=\sqrt{5^{2}+(4 + 8)^{2}}\).
\[y=\sqrt{25+144}=\sqrt{169}=13\]

Answer:

The value of \(x\) is \(\sqrt{89}\).
The value of \(y\) is \(13\).