In a right triangle, if one side is 5 and another side is 4, what is the angle adjacent to the side that measures 5?

To find the angle adjacent to the side that measures 5 in a right triangle where the other leg measures 4, we can use trigonometric functions. Specifically, we can utilize the cosine function, as it relates the adjacent side to the hypotenuse.

First, we determine the length of the hypotenuse using the Pythagorean theorem:

[

c = \sqrt{a^2 + b^2} = \sqrt{5^2 + 4^2} = \sqrt{25 + 16} = \sqrt{41}

]

Now, we can calculate the cosine of the angle adjacent to the side measuring 5:

[

\cos(\theta) = \frac{\text{Adjacent side}}{\text{Hypotenuse}} = \frac{5}{\sqrt{41}}

]

To find the angle, we take the arccosine (inverse cosine):

[

\theta = \arccos\left(\frac{5}{\sqrt{41}}\right)

]

Calculating this gives us an angle of approximately 38.66 degrees, which corresponds with the second option provided. Therefore, this angle represents the angle adjacent to the side measuring 5.