Question

find j.
triangle with right angle, two 45° angles, one leg 6√3 m, hypotenuse j
write your answer in simplest radical form.
blank meters
√ button

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 \(c = a\sqrt{2}\). Here, the leg length is \(6\sqrt{3}\) m, and \(j\) is the hypotenuse.

Step2: Apply 45 - 45 - 90 formula

Using \(c=a\sqrt{2}\), where \(a = 6\sqrt{3}\), we substitute:
\(j=6\sqrt{3}\times\sqrt{2}\)

Step3: Simplify the radical

Multiply the radicals: \(\sqrt{3}\times\sqrt{2}=\sqrt{6}\), so \(j = 6\sqrt{6}\)

Answer:

\(6\sqrt{6}\)