A right triangle has sides of length 5, 12 and 13. What is the sine of the angle opposite the hypotenuse?
(A) 1 (B) 5/12 (C) 5/13 (D) 12/13 (E) None of the above.
Mmmmh, aren't they asking for sin 90° ?
To find the sine of the angle opposite the hypotenuse, we need to remember that the sine is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.
In this case, we have a right triangle with sides of length 5, 12, and 13. The hypotenuse is the longest side, which is 13.
So, to find the sine of the angle opposite the hypotenuse, we need to find the length of the side opposite that angle. Let's label the sides of the triangle: side A = 5, side B = 12, and the hypotenuse C = 13.
Using the Pythagorean theorem, we can find the length of the side opposite the angle. The theorem states that for any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, we have:
A^2 + B^2 = C^2
5^2 + 12^2 = 13^2
25 + 144 = 169
169 = 169
The equation is true, so the lengths of the sides satisfy the Pythagorean theorem.
Now we know that side A is the side opposite the angle we're interested in. To find the sine of this angle, we divide the length of side A by the length of the hypotenuse.
Sine(angle) = A / C
Sine(angle) = 5 / 13
So, the sine of the angle opposite the hypotenuse is 5/13.
Therefore, the correct answer is (C) 5/13.