Question

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?

Answer 1

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)

Answer 2

Thank you!
Next question.

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