Help triangle within a circle find side of triangle

[kmiller]

The corners of an equilateral triangle lie on a circle of radius 2.9 m. Find the length of a side of the triangle.

find meters

 

[R.Harmon]

One way is to draw a line from each vertex of the triangle to the centre of the circle, splitting the equilateral triangle into 3 isosceles. If you consider one of these triangles, you can fairly easily work out all the internal angles, and you know the length of two of the sides of the isosceles triangle (the radius of the circle). From here you just use trigonometry to find the length of the third side, which is the length of the side of the triangle.

 

[thomate1]

To find the length of a side of the triangle, we can use basic trigonometric principles. Since the triangle is equilateral, all sides will be the same length. We can use the fact that the corners of the triangle lie on a circle of radius 2.9 m to create a right triangle, with one side being the radius and the other being half of a side of the equilateral triangle.

Using the Pythagorean theorem, we can set up the equation: (2.9)^2 = (0.5x)^2 + (x)^2, where x represents the length of a side of the triangle. Solving for x, we get x = 2.9√3 ≈ 5.02 m.

Therefore, the length of a side of the equilateral triangle is approximately 5.02 meters.