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

D = 23.7 miles

Explanation:

Given data:

`\theta=84 degrees`

Time
`= 20 min = (1)/(3) hr`

Distance of A
`= (60 mi/hr)* (1)/(3) hr =20 mi`

Distance of B =
`(45 mi/hr)(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* 20* 15* cos(84)`

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

`D^2 = 625 - 63.2`

`D^2 = 561.8`

Thus D = 23.7 miles