Question

solve for x to the nearest hundredth.
triangle image: right triangle with one angle 45°, hypotenuse 2√6, legs x and y

Explanation:

Step1: Identify Triangle Type

The triangle is a right triangle with one angle \(45^\circ\), so it's a \(45^\circ - 45^\circ - 90^\circ\) triangle (isosceles right triangle), meaning legs \(x\) and \(y\) are equal, and hypotenuse \(= x\sqrt{2}\).

Step2: Set Up Hypotenuse Formula

Given hypotenuse \(= 2\sqrt{6}\), so \(x\sqrt{2}=2\sqrt{6}\).

Step3: Solve for \(x\)

Divide both sides by \(\sqrt{2}\): \(x = \frac{2\sqrt{6}}{\sqrt{2}}\). Simplify \(\frac{\sqrt{6}}{\sqrt{2}}=\sqrt{3}\), so \(x = 2\sqrt{3}\). Calculate \(2\sqrt{3}\approx2\times1.732 = 3.464\), round to nearest hundredth: \(x\approx3.46\).

Answer:

\(3.46\)