A carpenter plans to make two small triangular tables by cutting the big table along the line AD. What will be the length of the side BD of the table ABD?

I know it has to do with special right triangles, but I don't have any idea of how to set anything up.

Question

A carpenter plans to make two small triangular tables by cutting the big table along the line AD. What will be the length of the side BD of the table ABD? 

I know it has to do with special right triangles, but I don't have any idea of how to set anything up.

anonymous · Answer

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anonymous · Answer

I'm not sure whether to use trigonometric ratios, or....?

anonymous · Answer

Do you remember the 30-60-90 triangle and 45-45-90 ratios?

anonymous · Answer

I know that in a 45-45-90 that the length of the legs are identical and the length of the hypotenuse is the length of a leg multiplied by the square root of two, and I know that in a 30-60-90 the length of the long leg ( side opposite the 60 ) is the length of the short leg ( opposite the 30 ) multiplied by the square root of three while the length of the hypotenuse is double the length of the short leg.

anonymous · Answer

Alright. Then you have no need for the trig ratios. If the side opposite the 60 is 90, what's the value of the side opposite the 30º?

anonymous · Answer

Like would the side opposite the 60 be 90 square root of 3 or is that the simplified version?

anonymous · Answer

Ok.
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Yes. Figure out what the side that has the question mark is. For instance, if we call that side x, then knowing the ratio:
$$x\sqrt{3} = 90$$$$x = \frac{90}{\sqrt{3}}$$$$x = \frac{90\sqrt{3}}{3}$$$$x = ?$$