Question

Los Angeles is 1,744 miles from Chicago, Chicago is 714 miles from New York, and New York is 2,451 miles from Los Angeles. Draw a triangle connecting these three cities, and find the angles in the triangle.

Answer 1

Following are the solution to this question:

Explanation:

please find the graph image in the attached file.

Given value:

`AB= c= 1744 \ miles\\\\BC= a= 2451 \ miles\\\\AB= s= 714 \ miles`

using the law of cosines:

`\cos A = (s^2+c^2-a^2)/(2bc)\\\\`

`=(714^2+1744^2-2451^2)/(2 * 714 * 1744)\\\\= -0.9862`

`A=cos^(-1) (-0.9862)\\\\A= 170.47^(\circ)`

`\cos B = (a^2+c^2-b^2)/(2ac)\\\\=(2451^2+1744^2-714^2)/(2 * 2451 * 1744)\\\\= 0.9988\\\\B=cos^(-1) (0.9988)\\\\B= 2.7641^(\circ)\\\\`

`\cos C = (a^2+c^2-b^2)/(2ac)\\\\=(2451^2+1744^2-714^2)/(2 * 2451 * 1744)\\\\= 0.9988\\\\C=cos^(-1) (0.9988)\\\\C= 2.7641^(\circ)`