A force of pounds makes an angle of with a second force. The resultant of the two forces makes an angle of to the first force. Find the magnitudes of the second force and of the resultant.

This question is incomplete, the complete question is;

A force of 193 pounds makes an angle of  79°14' with a second force. The resultant of the two forces makes an angle of 27°0' to the first force. Find the magnitudes of the second force and of the resultant.

magnitudes of the second force (vector) is 110.84 lb

the resultant force force has a magnitude of 239.85 lb

Explanation:

Given that;

Magnitude of resultant vector R = ?

Direction of resultant vector α = 27°0'

Magnitude of vector p = 193

Magnitude of vector Q = ?

Angle between two vectors ∅ = 79°14'

Using the formula

tan∝ = [ Qsin∅ / P + Qcos∅]

tan27°0' = [ Qsin79°14' / 193 + Qcos79°14' )

we cross multiply

(193tan27°0') + (Qcos79°14'tan27°0' ) = Qsin79°14'

Q = 193tan27°0' / (sin79°14' - cos79°14'tan27°0')

Q = 110.84 lb

Therefore magnitudes of the second force (vector) is 110.84 lb

Now

R = √( p² + Q² + 2PQcos∅ )

R = √( 193² + 110.84² + ( 2 × 193 × 110.84 × cos79°14'))

R = 239.85 lb

Therefore the resultant force force has a magnitude of 239.85 lb