Question

What is tan K?

please show your work

Answer 1

Since it’s angle K, 51 will be the hypotenuse, 45 will be the adjacent, and 24 will be the opposite. And since we’re looking for tan, which is the opposite over the adjacent, 24 is the opposite, and 45 is the adjacent. In conclusion, tan K = 24/45

Answer 2

In the given right-angled triangle with tan(K) = 24/51, the measure of angle K is approximately 25.1 degrees, calculated using the arctangent function.

In a right-angled triangle, the tangent of an angle is the ratio of the length of the side opposite the angle to the length of the adjacent side. In your case, if tan(K) = 24/51, this means the opposite side length is 24, and the adjacent side length is 51.

To find the degree measure of angle K, you can use the arctangent (inverse tangent) function on a calculator. The formula is:

Angle K = arctan(opposite side / adjacent side)

Substituting the values, you get:

Angle K = arctan(24/51) ≈ 25.1 degrees

So, the measure of angle K is approximately 25.1 degrees.