# trigonometry

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A ship sails 15.0 mi on a course S40°10’W and then 21.0 mi on a course N28°20’W. Find the distance and direction of the last position from the first.

• trigonometry -

if we indicate a path by (r,Ø) , where r is the distance and Ø is the direction measured counterclockwise from 0 at the normal position
then in component form (rcosØ,rsinØ we have
(15,S W40°10' W) = (15,229°50') = (-9.6752, -11.46257)

(21, N 28°20') = (21,118°20') = -9.9666, 18.4842)

add those two vectors for ( -19.6428, 7.021658)

magnitude = √(-19.6428^2+7.02168^2) = 20.859
direction:
tanØ = .7021.../-19.642.. = ..
Ø = W 19°40' N

check my arithmetic

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