Answer:
[tex]20^{\circ}[/tex]
Step-by-step explanation:
In any right triangle, the cosine of an angle is equal to its adjacent side divided by the hypotenuse.
Let the angle we want to find be [tex]\theta[/tex]. [tex]\theta[/tex]'s adjacent side is 49 and the hypotenuse of the triangle is 52.
Therefore, we have the equation:
[tex]\cos \theta=\frac{49}{52}[/tex]
Take the inverse cosine of both sides:
[tex]\arccos (\cos \theta)=\arccos(\frac{49}{52})[/tex]
Simplify using [tex]\arccos (\cos \theta)=\theta \text{ for }\theta \in (0, 180^{\circ})[/tex]:
[tex]\theta=\arccos(\frac{49}{52}),\\\theta=19.557214,\\\theta\approx \boxed{20^{\circ}}[/tex]
