Question

there is a right triangle with a right angle, one angle is 25 degrees, the adjacent side to the 25 - degree angle is 36, the hypotenuse is k, and there is a number 9 on the left side of the triangle.

Explanation:

Step1: Identify adjacent side and hypotenuse

In the right triangle, the side adjacent to the $25^\circ$ angle is 36, and $k$ is the hypotenuse. We use the cosine function: $\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$.

Step2: Rearrange to solve for $k$

Rearrange the cosine formula to isolate $k$: $k=\frac{\text{adjacent}}{\cos(\theta)}$
Substitute values: $k=\frac{36}{\cos(25^\circ)}$

Step3: Calculate the value

First, find $\cos(25^\circ)\approx0.9063$, then compute:
$k\approx\frac{36}{0.9063}\approx39.72$

Answer:

$k\approx39.72$ (rounded to two decimal places)