Find adjacent side of right triangle if the opposite side equals 12, and theta equals 36 degrees

Answer 1

To find the adjacent side of the right triangle, we will use the trigonometric function tangent.

The tangent of an angle in a right triangle is equal to the opposite side divided by the adjacent side. Therefore, we can use the formula:

tan(theta) = opposite/adjacent

In this case, theta is 36 degrees and the opposite side is 12. We are looking for the adjacent side, so we will rearrange the formula to solve for the adjacent side:

adjacent = opposite/tan(theta)

adjacent = 12 / tan(36)

Using a calculator, we can find the tangent of 36 degrees:

tan(36) ≈ 0.7265

Now, we can calculate the adjacent side:

adjacent ≈ 12 / 0.7265 ≈ 16.51

Therefore, the adjacent side of the right triangle is approximately 16.51 units.