Question

find v.
image of a right triangle with a 45° angle, one leg labeled 2 mi, hypotenuse labeled v, and the right angle marked
write your answer in simplest radical form.
blank miles
radical symbol button
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Explanation:

Step1: Identify Triangle Type

The triangle is a right - isosceles triangle (two angles are \(45^{\circ}\), so the two legs are equal). The hypotenuse is given as \(2\) miles. For a \(45 - 45 - 90\) triangle, the ratio of leg : hypotenuse is \(1:\sqrt{2}\). Let the length of each leg (including \(v\)) be \(x\). Then the hypotenuse \(h=x\sqrt{2}\).

Step2: Solve for \(v\)

We know that \(h = 2\) and \(h=x\sqrt{2}\), where \(x = v\). So we have the equation \(v\sqrt{2}=2\). To solve for \(v\), we divide both sides of the equation by \(\sqrt{2}\): \(v=\frac{2}{\sqrt{2}}\). Rationalizing the denominator (multiplying numerator and denominator by \(\sqrt{2}\)), we get \(v = \frac{2\sqrt{2}}{2}=\sqrt{2}\).

Answer:

\(\sqrt{2}\)