Trigonometry help...

[arizona 10+ year member]

So I am given this problem....

Two trains leave the railroad station at 12:30 pm. The first train travels along a straight track at 90 mph. The second train travels at 75 mph along another track that makes an angle of 130 degrees with the first track. At what time are the trains 400 miles apart.

So if you set up a triangle you get an obtuse triangle with an angle of 130 and the side opposite of it will be 400 miles long. But in order to solve the triangle and do all of the math to figure out the time part I need another side or angle measure. I am sure I am overlooking how to get that other angle or side... any suggestions?

I don't need the entire problem solved, just help on what to do to get that next piece of information.

Thanks.

Click to read more...

 

[tuomas 10+ year member]

Since it is similar to a "related rates problem" in calculus

(all you need to know is that the unknown side is increasing at a rate proportional to the other sides)

: C = sqrt[90^2 + 75^2 - 2(90)(75)cos(130)]

Once you have C, that is the MPH that the two trains are traveling away from each other based on their speeds. Take 400Miles and divide by C and you will have time that they will be 400 miles apart

so your answer should be roughly 149mph for side C, and they will be 400 miles apart at time 2.68 hours