Find the value of each variable. Write your answer in simplest radical form.

Question

A right triangle with 60° angles. X and Y are congruent and the hypotenuse is 4.

Answer 1

A right triangle can only have one 60 degree angle. "With 60 degree angles" is misleading.

If a right triangle has one 60 degree angle, the third angle is 30 degrees.

If you have a 30/60/90 right triangle, and you know the length of one side (h), you can express the lengths of the other sides (X and Y) with the sine law. One useful shortcut to remember: in a 30/60/90 right triangle, the length of one side is 1/2 the length of the hypotenuse (sin 30 = opposite/hypotenuse = 0.5). You can use this fact and the pythagorean theorem to figure the length of the third side.