# Strange trig problem

#### 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 in to the castle?

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

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#### 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,

Last edited:

#### HallsofIvy

Homework Helper
You are right. The information given is contradictory.

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