A 30-60-90 triangle has a 45-45-90 triangle attached such that the side opposite the 60° angle of the first is the hypotenuse of the second. If the shortest side of the 30-60-90 triangle is 4, what is each leg of the 45-45-90 triangle?

Question

Accepted Answer

2\sqrt{6}

Side opposite 60° in 30-60-90 = 4\sqrt{3}. This is the 45-45-90 hypotenuse, so each leg = \frac{4\sqrt{3}}{\sqrt{2}} = \frac{4\sqrt{3} \cdot \sqrt{2}}{2} = 2\sqrt{6}.

Answer

4\sqrt{2}

Answer

2\sqrt{3}

Answer

4\sqrt{3}

Answer

2\sqrt{6}

Lines, Angles, and Triangles

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