Question

A triangular city lot bounded by three streets has a length of 300 feet on one street, 250 feet on the second, and 420

feet on the third. Find the approximate measure of the largest angle formed by these streets.

Answer 1

The approximate measure of the largest angle formed by these streets is
`99.2\°`

Explanation:

we know that

Applying the law of cosines

`c^(2)=a^(2)+b^(2) -2(a)(b)cos(C)`

In this problem we have

`a=300\ ft`

`b=250\ ft`

`c=420\ ft` ----> is the greater side

substitute and solve for angle C

`420^(2)=300^(2)+250^(2) -2(300)(250)cos(C)`

`176,400=152,500 -150,000cos(C)`

`cos(C)=[152,500-176,400]/150,000`

`cos(C)=-0.1593`

`C=arccos(-0.1593)=99.2\°`