Using the technique in the model above, find the missing sides in this 30°-60°-90° right triangle. hypotenuse = 10 long =

5√3

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

5√3