Answer:
[tex]\cos(B) = \dfrac{2}{\sqrt{13}}[/tex]
Step-by-step explanation:
We are given the following side lengths:
We can solve for c with the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
↓ plugging in the given side lengths
[tex]2^2+3^2 =c^2[/tex]
↓ taking the square root of both sides
[tex]c = \sqrt{2^2 + 3^2}[/tex]
↓ simplifying the square root
[tex]c=\sqrt{13}[/tex]
Next, we can solve for cos(B) using the definition of the cosine ratio:
[tex]\cos(\theta)=\dfrac{\text{adjacent}}{\text{hypotenuse}}[/tex]
↓ plugging in the given side lengths and angles
[tex]\boxed{\cos(B) = \dfrac{2}{\sqrt{13}}}[/tex]
