Question

Pleas help me with this question

Answer 1

`\large\boxed{\cos\beta=(5)/(13)}`

Explanation:

Use the cosine law:

`b^2=a^2+c^2-2ac\cos\beta\\\\\text{We have:}\\\\b=48,\ a=20,\ c=52\\\\\text{Substitute:}\\\\48^2=20^2+52^2-2(20)(52)\cos\beta\\2304=400+2704-2080\cos\beta\\2304=3104-2080\cos\beta\qquad\text{subtract 3104 from both sides}\\-800=-2080\cos\beta\qquad\text{divide both sides by 2080}\\(800)/(2080)=\cos\beta\\\\\cos\beta=(80)/(208)\to\cos\beta=(80:16)/(208:16)\to\cos\beta=(5)/(13)`