Question

Two corners of a triangle have angles of `(3 pi ) / 8` and `pi / 4`. If one side of the triangle has a length of `1`, what is the longest possible perimeter of the triangle?

Answer 1

`color(blue)("Longest possible Perimeter of " Delta = a + b + c = 3.62 " units"`

Explanation:

`hat A = (3pi)/8, hat B = pi/4, hat C = pi - (3pi)/8-pi/4 = (3pi)/8`

It's an isosceles triangle with sides a & c equal.

To get the longest possible perimeter, length 1 should correspond to #hat B3, the least angle.

`;. 1 / sin (pi/4) = a / sin ((3pi)/8) = c / sin ((3pi)/8)`

`a = c = (1 * sin ((3pi)/8)) / sin (pi/4) = 1,31`

`"Perimeter of the " Delta = a + b + c = 1.31 + 1 + 1.31 = 3.62`