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

Answer:

Following are the solution to this question:

Step-by-step 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:  

$\cos A = \frac{s^2+c^2-a^2}{2bc}$

        $=\frac{714^2+1744^2-2451^2}{2 \times 714 \times 1744}\\\\= -0.9862$

$A=cos^{-1} (-0.9862)\\\\A= 170.47^{\circ}$

$\cos B = \frac{a^2+c^2-b^2}{2ac}\\\\=\frac{2451^2+1744^2-714^2}{2 \times 2451 \times 1744}\\\\= 0.9988\\\\B=cos^{-1} (0.9988)\\\\B= 2.7641^{\circ}$

$\cos C = \frac{a^2+c^2-b^2}{2ac}\\\\=\frac{2451^2+1744^2-714^2}{2 \times 2451 \times 1744}\\\\= 0.9988\\\\C=cos^{-1} (0.9988)\\\\C= 2.7641^{\circ}$