Given that the hypotenuse of this right triangle is 25 cm long and that tan (θ) = 3find the values of x and y, accurate to the nearest tenth.

The tangent of an angle is the opposite side divided by the adjacent side of the triangle, relative to the angle. By tan theta = 3, it means that, the adjacent side is thrice as long as the opposite side.

3a = o

Then, using Pythagorean's theorem:

25² = a² + o²

Substituting o,

25² = a² + (3a) ²

25² = a² + 9a²

25² = 10a²

a = 7.9 cm

Then, 3 (7.9) = o = 23.7 cm

So, the opposite side is 23.7 cm and the adjacent side is 7.9 cm.