right triangle ABC has side lengths AB=21, BC=28 and AC=35. Find the ratio of the side opposite <C to the hypotenuse of triangle ABC.
Let the side opposite angle C be denoted as c.
By the Pythagorean theorem, we know that in a right triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse.
So, in this case, we have:
AB^2 + BC^2 = AC^2
21^2 + 28^2 = 35^2
441 + 784 = 1225
1225 = 1225
Therefore, we can conclude that triangle ABC is a right triangle.
To find the ratio of the side opposite angle C to the hypotenuse, we divide the length of side c by the length of the hypotenuse.
Using the values given, c = BC = 28 and the hypotenuse is AC = 35.
Therefore, the ratio of side c to the hypotenuse is:
c/AC = 28/35 = 4/5
So, the ratio of the side opposite angle C to the hypotenuse of triangle ABC is 4/5.