Question

Find the missing lengths. Leave your answer in simplest radical form

Answer 1

The right triangle has one angle = 60° and the second, 30°, then it is also a semi equilateral one & the side (y) opposed to the angle of 30° is equal to half of the hypotenuse (x).

Calculate x by Pythagoras:

x² = (5√3)² + y², but y = x/2==> y² =(x/2)² =x²/4

x² = 75 + x²/4 ==> 4x² = 300 + x²==> 3x²=300, x² =100 and x=10 and y =5