Suppose a camping tent has a center pole that is 6 feet high. if the sides of the tent make 40 degree angles with the ground, how wide, in feet, is the tent

We assume that the tent is in a triangular shape. We divide the triangle into two right triangles where the angles are 90° , 40° and 50°. We are given one side of the triangle which is 6 ft, the height of the center pole. We can use the tangent trigonometric function to solve for the base of one right triangle.

tan α = opposite side / adjacent side = pole height / base of one right triangle

tan 40° = 6 ft / base of one right triangle
Base of one right triangle = 7.15 ft

Multipliying it by 2, we get the total width of the tent. Which is,
Width of the tent = 14.30 ft

It’s hard to understand what you put.. can you show a picture ?