Question

find f.
√6 km, 45°, 45°, f (right triangle)
write your answer in simplest radical form.
kilometers
√ (button)
submit

Explanation:

Step1: Identify Triangle Type

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

Step2: Apply 45 - 45 - 90 Ratio

Here, the hypotenuse is \(\sqrt{6}\) km, and \(f\) is a leg. Using \(a=\frac{c}{\sqrt{2}}\), substitute \(c = \sqrt{6}\):
\(f=\frac{\sqrt{6}}{\sqrt{2}}\)
Simplify the radical: \(\frac{\sqrt{6}}{\sqrt{2}}=\sqrt{\frac{6}{2}}=\sqrt{3}\) (since \(\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}\) for \(a,b>0\)).

Answer:

\(\sqrt{3}\)