Answer:
The approximate measure of the largest angle formed by these streets is [tex]99.2\°[/tex]
Step-by-step explanation:
we know that
Applying the law of cosines
[tex]c^{2}=a^{2}+b^{2} -2(a)(b)cos(C)[/tex]
In this problem we have
[tex]a=300\ ft[/tex]
[tex]b=250\ ft[/tex]
[tex]c=420\ ft[/tex] ----> is the greater side
substitute and solve for angle C
[tex]420^{2}=300^{2}+250^{2} -2(300)(250)cos(C)[/tex]
[tex]176,400=152,500 -150,000cos(C)[/tex]
[tex]cos(C)=[152,500-176,400]/150,000[/tex]
[tex]cos(C)=-0.1593[/tex]
[tex]C=arccos(-0.1593)=99.2\°[/tex]
