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MATH / A 30^(∘)-60^(∘)-90^(∘) triangle is drawn on the exterior of an equilateral triangle so the hypotenuse of the right triangle is one side of the equilateral triangle. If the shorter …

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

A 30∘30^\circ-60∘60^\circ-90∘90^\circ triangle is drawn on the exterior of an equilateral triangle so the hypotenuse of the right triangle is one side of the equilateral triangle. If the shorter leg of the right triangle is 6 units, what is the distance between the two vertices that the triangles do not have in common? Express your answer in simplest radical form. [asy] draw((2,0)--(0,0)--(1,1.732)--(2,1.732)--(2,0)--(1,1.732)); draw((2,1.632)--(1.9,1.632)--(1.9,1.732)); label("60∘60^\circ",(1,1.732),2SE+E); label("30∘30^\circ",(2,0),5NNW+4N); label("6",(1.5,1.732),N); [/asy]
Plain-text mathematical notation (without MathML)
A 30^(∘)-60^(∘)-90^(∘) triangle is drawn on the exterior of an equilateral triangle so the hypotenuse of the right triangle is one side of the equilateral triangle. If the shorter leg of the right triangle is 6 units, what is the distance between the two vertices that the triangles do not have in common? Express your answer in simplest radical form. [asy]
draw((2,0)--(0,0)--(1,1.732)--(2,1.732)--(2,0)--(1,1.732));
draw((2,1.632)--(1.9,1.632)--(1.9,1.732));
label("60^(∘)",(1,1.732),2SE+E);
label("30^(∘)",(2,0),5NNW+4N);
label("6",(1.5,1.732),N);
[/asy]
Original LaTeX notation
A $30^\circ$-$60^\circ$-$90^\circ$ triangle is drawn on the exterior of an equilateral triangle so the hypotenuse of the right triangle is one side of the equilateral triangle. If the shorter leg of the right triangle is 6 units, what is the distance between the two vertices that the triangles do not have in common? Express your answer in simplest radical form. [asy]
draw((2,0)--(0,0)--(1,1.732)--(2,1.732)--(2,0)--(1,1.732));
draw((2,1.632)--(1.9,1.632)--(1.9,1.732));
label("$60^\circ$",(1,1.732),2SE+E);
label("$30^\circ$",(2,0),5NNW+4N);
label("6",(1.5,1.732),N);
[/asy]

level

Level 5

type

Prealgebra

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Source and history

task_id
22527db3-2a83-58df-ab98-82bfcb84d0b1
task_key
prealgebra--test--22527db3-2a83-58df-ab98-82bfcb84d0b1
task_revision_id
1
config / split
prealgebra / test

Official source

initial import