Azimuth at Treasure Island

Problem #98

Tags: geometry loops

Who solved this?

A group of pirates was lucky to lay their hands on the map of the Treasure Island.

To their disappointment the map does not contain a vague drawings with a small black cross - but instead just several lines like the following:

Pirates read in Wikipedia that azimuth 0 is the direction to the North, azimuth 90 is the direction to the East and so on.

However, they use a kind of GPS-navigator in place of compass. Instead of directions the device can show coordinates or offsets in feets.

So pirates need to solve the following problem: suggesting that the point of "the pole with the plaque Start" is the origin of coordinate system with Y axis pointing to the North and X axis pointing to the East - what are the coordinates of the treasure point?

Input data will be in format close to the directions inscribed on a map:
The first line contains words Stand at the pole with the plaque START - you can safely ignore this.
Next lines contain words go X feet by azimuth Y - you are to extract numbers from them.
Last line contains phrase Dig here!
Answer should contain coordinates of the point where the Treasure is hidden, rounded to closest integers.


input data:
Stand at the pole with the plaque START
go 140 feet by azimuth 332
go 460 feet by azimuth 78
Dig here!

384 219
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