Answer:
The distance between Mercer and Turtle Lake is 25.57 km
Step-by-step explanation:
Law of cosines
When a triangle is defined by two of its sides and the angle formed by them, we can apply the law of cosines to know the third side. Being a and b the known sides and [tex]\alpha[/tex] the angle, we write the law of cosines as
[tex]\displaystyle c^{2}=a^{2}+b^{2}-2ab\cos \alpha[/tex]
In our case:
[tex]a=24 km,\ b=17 km ,\ \alpha=75^o[/tex]
[tex]\displaystyle c^{2}=24^2+17^2-2(24)(17)\cos 75^o[/tex]
[tex]\displaystyle c^{2}=653.804[/tex]
[tex]\displaystyle c=25.57\ km[/tex]
The distance between Mercer and Turtle Lake is 25.57 km
