Question

A map suggests that Atlanta is 730 miles in a direction of

Answer 1

Answer:

The displacement from Dallas to Chicago is 788 miles.

Explanation:

Given that,

A map shows that,

Atlanta is 730 miles in a direction of 5.00° north of earth from Dallas.

Same map shows that,

Chicago is 560 miles in a direction of 21.0° west of north from Atlanta.

We need to calculate the displacement from Dallas to Chicago

We need to figure,

In figure,

C = Atlanta

B = Chicago

A = Dallas

Using cosine law,

$c=\sqrt{a^2+b^2-2ab\cosC}$

Where, a = distance between Dallas to Atlanta

b = distance between Atlanta to Chicago

Put the value into the formula

$c=\sqrt{(560)^2+(730)^2-2\times560\times730\cos74}$

$c=788\ miles$

Hence, The displacement from Dallas to Chicago is 788 miles.