Find the exact value of the trigonometric function given the right triangle. The adjacent side is 7, and the opposite side is 4.

Answer 1

To find the exact value of the trigonometric function, we can use the Pythagorean theorem to find the length of the hypotenuse first.

Using the Pythagorean theorem:
c^2 = a^2 + b^2
c^2 = 7^2 + 4^2
c^2 = 49 + 16
c^2 = 65
c = sqrt(65)

Now, we can find the trigonometric function cosine of angle A:
cos(A) = adjacent side / hypotenuse
cos(A) = 7 / sqrt(65)

Therefore, the exact value of the trigonometric function cosine of angle A is 7/sqrt(65).