if cosB = 2/4 and the opposite is 200, then what is hypotenuse and adjacent?

First, let's clarify that cosB = 2/4 simplifies to cosB = 0.5.

The cosine of an angle in a right triangle is defined as the ratio of the adjacent side to the hypotenuse. So if cosB = 0.5, this means that the ratio of the adjacent side to the hypotenuse is 0.5.

Given that the opposite side is 200, we can use the Pythagorean theorem to find the hypotenuse. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

However, we don't have enough information to use the Pythagorean theorem yet, because we don't know the length of the adjacent side.

We can find the length of the adjacent side using the definition of cosine. If cosB = 0.5, and cosB is the ratio of the adjacent side to the hypotenuse, then the adjacent side is 0.5 times the length of the hypotenuse.

Let's denote the hypotenuse as H and the adjacent side as A. We then have the equation A = 0.5H.

We can substitute A into the Pythagorean theorem:

200^2 + (0.5H)^2 = H^2 40000 + 0.25H^2 = H^2

Solving this equation for H gives H = sqrt(40000 / 0.75) = 200 * sqrt(4/3) = 200 * 2/sqrt(3) = 400/sqrt(3) = 400*sqrt(3)/3.

Substituting H = 400sqrt(3)/3 into the equation A = 0.5H gives A = 0.5 * 400sqrt(3)/3 = 200*sqrt(3)/3.

So, the hypotenuse is 400sqrt(3)/3 and the adjacent side is 200sqrt(3)/3.