Posted by **SummerHomework** on Wednesday, July 25, 2012 at 3:32pm.

I am catching up over summer on math units that I have to rewrite. In my textbook it asks me to find the base of two triangles and add them together. the smallest angle of the larger triangle is 30 degrees. The opposite side to the angle is 40cm. it gives me Tan 30 = 40/x

1/square root of 3 = 40/x

40 *(squareroot of 3)

My question is, how did my textbook get 1/sq.rt. of 3 as Tan 30?

- Radicals and Trig. -
**drwls**, Wednesday, July 25, 2012 at 10:08pm
Because that is the value of tan 30 . The short side length is half the hypotenuse for a 30-60-90 triangle.

If the hypotenuse length is 1, the Second longest side length must be sqrt[3/4]

That makes the tangent of 30 degrees 1/(sqrt3)

- Radicals and Trig. -
**SummerHomework**, Friday, July 27, 2012 at 10:50am
Thank you!

Next question.

What if instead they gave me the hypotenuse? 2/(sqrt2? Still tan 30.

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