Solve a Strange Trig Problem: Distance to a Castle Spotted by Two Men in a Car

[danne89]

A car travels with a velocity of 90 km/h on a stright line. And a man in the car saw a castle left of the road. The angle the straight line to the castle from the cars position was 30 degrees. 15 min (same vel) later another man spots the castle in an 40-degrees angle. After another 15 min they spot a perpendicular way towards the castle. How long is this way into the castle?

tan 30 degrees = x/45 => x=~ 30 km
tan 40 degrees = x/22.5 => x~= 19 km
??

 

[wisredz]

Have you tried to draw the problem to help you understand better? What progress have you made?

 

[danne89]

I'm sorry. I was in a hurry when I tried to descibe my progress. I indeed draw a picture and obtained those equations above. My point is that they contridict each other.

 

[Muzza]

15 min (same vel) later another man spots the castle in an 40-degrees angle

And this other man, where is he located?

 

[danne89]

In the car he also.

So you have two right triangles with a common side, the road to the castle. One has an angle of 30 degrees and a side of 45 km. The other triangle has a angle of 40 degrees and a side of 22.5 km,

 

[HallsofIvy]

You are right. The information given is contradictory.