Answer: 5√3
Step-by-step explanation:
1) Technique: using known ratios of triangles 30° - 60° - 90°.
2) Since, for all the the triangles 30° - 60° - 90° the ratios of the sides are:
long side : short side : hypotenuse = √3 : 1 : 2,
3) Then, you can set the proportion with the long side and the short side, which is:
long side √3
---------------- = -----
hypotenuse 2
4) Solve for the long side:
long side = hypotenuse * (√3) / (2)
5) Replace the value of hypotenuse = 10
long side = 10 * (√3) / 2 = 5√3
Answer: 5√3