Answer:
C. 74°
Step-by-step explanation:
Cosine Rule (for finding angles)
[tex]\sf \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]
where:
- C = angle
- a and b = sides adjacent the angle
- c = side opposite the angle
Given:
- C = [tex]\theta[/tex]
- a = 5
- b = 11
- c = [tex]\sf \sqrt{115}[/tex]
Substitute these values into the formula:
[tex]\implies \sf \cos(\theta)=\dfrac{5^2+11^2-(\sqrt{115})^2}{2(5)(11)}[/tex]
[tex]\implies \sf \cos(\theta)=\dfrac{25+121-115}{110}[/tex]
[tex]\implies \sf \cos(\theta)=\dfrac{31}{110}[/tex]
[tex]\implies \sf \theta=\cos^{-1}\left(\dfrac{31}{110}\right)[/tex]
[tex]\implies \sf \theta=74^{\circ} \quad (nearest\:degree)[/tex]
