Final answer:
To find the length of the adjacent side x in the triangle described, we use the cosine function. Cosine of 60° is 0.5, so setting up the equation 0.5 = x / (8√3) and solving for x, we find that the length of side x is 4√3 cm.
Step-by-step explanation:
The student is asking about the length of the adjacent side x in a right triangle, where the hypotenuse is given as 8√3 cm and one of the angles is 60°. To find the adjacent side in a right-angled triangle, we can use trigonometric ratios. Since we are dealing with the adjacent side and hypotenuse, the cosine function is appropriate here.
Using the cosine function, we know that cos(60°) = x / (8√3). Since cos(60°) = 0.5, we can write the equation as 0.5 = x / (8√3). Solving for x, we multiply both sides by 8√3 to get x = 4√3 cm.
Therefore, the length of the adjacent side x in its simplest form is 4√3 cm.