record distances to the nearest 001 ft and angles in degrees

record distances to the nearest 0.01
ft. and angles in degrees, minutes and seconds (to the nearest seconds)

show steps

Solution

angle C = 48.2825

applying law of cosines to find the side opposite to angle C

c = sqrt ( 371.21^2 + 339.06^2 - 2* 371.21*339.06 )

c = 291.969

now applying law of sines

c / sin C = a / sin A

A = sin ^-1 [ 371.21 sin ( 48.2825) / 291.969)]

A = 71.626 degrees

A = 71 degrees 37\' 33.6\"