Question

question 10 of 50
the value of x is:
triangle with right angle, two 45° angles, hypotenuse 16√2, side x
options: 16, 16√3, 8

Explanation:

Step1: Identify Triangle Type

The triangle has a right angle and two \(45^\circ\) angles, so it's a 45 - 45 - 90 (isosceles right) triangle. In such a triangle, the legs are equal, and the hypotenuse \(h\) is related to a leg \(l\) by \(h = l\sqrt{2}\).

Step2: Relate Hypotenuse and Leg

Here, the hypotenuse is \(16\sqrt{2}\), and \(x\) is a leg. Let the leg length be \(x\). From the formula \(h = x\sqrt{2}\), we solve for \(x\):
\(x=\frac{h}{\sqrt{2}}\). Substituting \(h = 16\sqrt{2}\), we get \(x=\frac{16\sqrt{2}}{\sqrt{2}}\).

Step3: Simplify the Expression

The \(\sqrt{2}\) terms cancel out: \(\frac{16\sqrt{2}}{\sqrt{2}} = 16\).

Answer:

16 (corresponding to the option "16")