Question

Right triangle ABC, with one 60-degree angle is inscribed in a circle. If the area of the circle is 256pi, what is the perimeter of the triangle? Leave your answer in the format: (2+3root5)

Answer 1

Answer:

Step-by-step explanation:

radius r = √256 = 16

Hypotenuse of the triangle is a diameter of the circle.

hypotenuse = 2r = 32

Sides of a 30-60-90 are in the ratio 1:√3:2

side opposite the 30° angle = 32/2 = 16

side opposite the 60° angle = 16√3

Perimeter = 48+16√3 units