Question

Find the adjacent side of a right triangle if the hypotenuse is unknown, the opposite side is 12, and theta is 36 degrees

Answer 1

To find the length of the adjacent side of a right triangle, we will use the trigonometric function cosine.

cos(theta) = adjacent / hypotenuse

In this case, theta = 36 degrees and the opposite side is given as 12.

cos(36) = adjacent / hypotenuse

Using the cosine of 36 degrees (which is approximately 0.809), we have:

0.809 = adjacent / hypotenuse

To isolate the adjacent side, we need to multiply both sides of the equation by the hypotenuse:

0.809 * hypotenuse = adjacent

Since the hypotenuse is unknown, we will denote it as h:

0.809 * h = 12

Now, we can solve for the hypotenuse by dividing both sides by 0.809:

h = 12 / 0.809

h ≈ 14.85

Therefore, the length of the adjacent side of the right triangle is approximately 14.85.