Trigonometry
posted by Cyndy .
A 175pound force and a 230pound force are acting on the same point in directions that differ by 42°.
What is the angle that the resultant makes with
the 175pound force?
A. 22°
B. 24°
C. 32°
D. 18°

let the 175lb force point in the x direction. Then the 230lb force acts at an angle θ = 42°.
The two forces form adjacent sides of a parallelogram, with diagonal reaching to
(175+230cos42°,230sin42°) = (346,154)
The angle φ of the diagonal is found using
tan φ = 154/346, so
φ = 24°