Solving a 30º-60º-90º Triangle
An equilateral triangle has sides of length 6. What is the length of the altitude, as drawn below?
Incorrect.
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The side across from the 30 degree angle will have a length of 3.
The altitude is across from the 60 degree angle.
Correct.
An equilateral triangle will have interior angles of 60 degrees. When the altitude is drawn, it forms two 30-60-90 recycled right triangles.
30-60-90 recycled right triangles have sides that always form the same ratio.
$$\displaystyle a$$:$$a\sqrt{3}$$:$$2a$$.
For these triangles, the hypotenuse (2_a_) is the same as the side of the original equilateral triangle (6).
Therefore,
$$\displaystyle a=3$$ and the altitude is $$3\sqrt{3}$$.
Incorrect.
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The hypotenuse has a length of 6, so the altitude must be shorter than 6.
Incorrect.
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This answer is a distractor that is trying to confuse you with 45-45-90 recycled right triangles.
Incorrect.
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This answer can be eliminated because
$$\displaystyle 6\sqrt{3}$$ is larger than $$6$$.
The hypotenuse has a length of 6, so the altitude must be shorter.
$$3$$
$$3\sqrt{3}$$
$$6$$
$$6\sqrt{2}$$
$$6\sqrt{3}$$
