If the terminal side of theta in standard position contains the point (5,8). Find the exact value of tan of theta

Huh?

tan theta = 8/5 !!!

To find the exact value of tangent (tan) of theta, we can use the coordinates of the point (5, 8) on the terminal side of theta in standard position.

First, let's mark the point (5, 8) on the coordinate plane.

Next, we can draw a right triangle by connecting the origin (0, 0) to the point (5, 8).

The hypotenuse of the right triangle will be the straight line connecting the origin to the point (5, 8), and the legs of the right triangle will be the horizontal and vertical distances from the origin to the point (5, 8).

Using the Pythagorean theorem, we can calculate the length of the hypotenuse as follows:

Hypotenuse² = Base² + Height²

In this case, the base is 5 and the height is 8, so:

Hypotenuse² = 5² + 8²
Hypotenuse² = 25 + 64
Hypotenuse² = 89

To find the length of the hypotenuse, we take the square root of both sides:

Hypotenuse = √89

Now, we can calculate the value of tangent (tan) of theta by dividing the height (8) by the base (5):

tan(theta) = Height / Base
tan(theta) = 8 / 5

Therefore, the exact value of tangent (tan) of theta is 8/5 or 1.6.

1.6