Answer:
x = 22.62° (nearest hundredth)
Step-by-step explanation:
As this is a right triangle, we can use the cosine trigonometric ratio to find x.
[tex]\sf \cos(\theta)=\dfrac{A}{H}[/tex]
where:
- [tex]\theta[/tex] is the angle
- A is the side adjacent the angle
- H is the hypotenuse (the side opposite the right angle)
Given:
- [tex]\theta=x[/tex]
- A = 12
- H = 13
Substitute the given values into the formula and solve for x:
[tex]\implies \cos(x)=\dfrac{12}{13}[/tex]
[tex]\implies x=\cos^{-1}\left(\dfrac{12}{13}\right)[/tex]
[tex]\implies x=22.61986495...^{\circ}[/tex]
[tex]\implies x=22.62^{\circ}\:\: \sf(nearest\:hundredth)[/tex]
