Question

A jet leaves Reno, Nevada and is headed toward Miami, Florida at a bearing of 100°. The distance between the two cities is approximately 2472 miles.
(a) How far north and how far west is Reno relative to Miami? (Round your answers to two decimal places.)

miles north

miles west

(b) If the jet is to return directly to Reno from Miami, at what bearing should it travel?

°

Answer 1

So hmm, if you notice the picture below

"y" would be the opposite to the 10° angle, and "x" would its adjacent

Reno is "y" north and "x" west from Miami

$\bf sin(\theta)=\cfrac{opposite}{hypotenuse}\implies sin(10^o)=\cfrac{y}{2472}$  solve for "y", to see how much north

and $\bf cos(\theta)=\cfrac{adjacent}{hypotenuse}\implies cos(10^o)=\cfrac{x}{2472}$  solve for "x" to see how much west

make sure, that in both cases, your calculator is in Degree mode, since the angle is in degrees, as opposed to Radian mode


now... for the section B)

if notice the Reno-Miami line, and you were to draw a North line through it, anywhere in between, or at an endpoint like the in the picture at Reno, the "clockwise" angle, will always be the same, 100°

bear in mind ( no pun intended ), that Bearings use the North line, and the clockwise angle from it, as in the picture below