Question

I got the answer but I don't know how to show my work, can ya'll tell me what I should write

Answer 1

Note: the hypotenuse is 16, not 1

Without trigonometry:

If you flip the triangle over the horizontal side you get an equilateral triangle. The "vertical" side of the new triangle is made of two segment of length 8, so it's 16 in total, which is the same - since it's an equilateral triangle - as the hypotenuse of the half triangle. The horizontal side is found with pythagorean theorem:

`8^2+x^2 = 16^2 \rightarrow x^2 = (2*8)^2-8^2 =(4-1)* 8^2 = 3*8^2\\x=8\sqrt3`

With trigonometry:

Call a the hypotenuse, b the horizontal side length b.

`sin30 = \frac8a \rightarrow a= \frac8{sin30} = \frac8{\frac12} = 16\\cos30= (b)/(a) \rightarrow b=a\ cos30 = 16 (\frac{\sqrt3}2)=8\sqrt3`