Question

two automobiles leave a city at the same time and travel along straight highways that differ in direction by 84 degrees. if their speeds are 60 mi/hr and 45 mi/hr, approximatly how far apart are the cars at the end of 20 minutes?

Answer 1

Answer:

D = 23.7 miles

Step-by-step explanation:

Given data:

$\theta=84 degrees$

Time$= 20 min = \frac{1}{3} hr$

Distance of A $= (60 mi/hr)\times \frac{1}{3} hr =20 mi$

Distance of B =$(45 mi/hr)\frac{1}{3} hr = 15 mi$

Draw a triangle.

By using cosine formula we can determine the distance between them

$D^2 = 20^2 + 15^2 - 2\times 20\times 15\times cos(84)$

$D^2 = 625 - 600 cos(84)$

$D^2 = 625 - 63.2$

$D^2 = 561.8$

Thus D = 23.7 miles