30-60-90 triangle question

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30-60-90 triangle question

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Other answers:

This is more properties of a 30-60-90 triangle than Pythagorean theorem.
Do you know the relationship of sides of a 30-60-90 triangle?
YES
Can you draw it using the draw tool?
ok i already know the answer and it showed me it but can you explain how the answer was worked out?
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|dw:1433881486021:dw|
ok, but i don't know how to solve it
They gave you the side opposite the right angle as \(\sf 8\sqrt{3}\) And so if we look at the drawing I posted, and correlate the sides to solve for a we get: \(\sf 2a = 8\sqrt{3}\) \(\sf\Large a=\frac{8\sqrt{3}}{2}=4\sqrt{3}\)
and you can see that the side that they want is the side opposite the angle 60 In the drawing I posted, it has a value of \(\sf a\sqrt{3}\) and we calculated a as \(\sf 4\sqrt{3}\) So if we plug in the value of a, we get: \(\sf 4 \sqrt{3}\times \sqrt{3}=4 \times 3 = 12\)
The side opposite 30 degrees is always half of the hypotenuse. So if the hypotenuse is \[8\sqrt{3}\] then the side opposite to the 30 degees would be \[\frac{8\sqrt{3}}{2}\] which is \[4\sqrt{3}\] And the 60 degrees side is always the 30 degrees side times sqrt 3. So it would be \[4\sqrt{3}*\sqrt{3}\] which is the same as \[4\sqrt{9}\] which is \[4*3\] which obviously get you 12.

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