Question

A design is formed by joining isosceles right triangles and 60°-30° right triangles as shown in the diagram. If the hypotenuse of the 60°-30° triangle is 12 centimeters, which is closest to the length of one leg of the isosceles right triangle?

Answer 1

For a 60°-30°, the length of the side opposite the 30° is equal to 1/2 of the hypotenuse. Also, the length of the side opposite the 60° is equal to the product of the hypotenuse and √3/2. 
Therefore from this, the value of the sides opposite to 30° and 60° are 6 cm and 10.39 cm, respectively.