find projection

Question

Forces of 5 pounds and 19 pounds act on each other with an angle of 48°.

The magnitude of the resultant force ≈ ____ pounds.

The resultant force has an angle of ≈ ____° with the 5 pound force.

The resultant force has an angle of ≈ _____° with the 19 pound force.

I know how to do the magnitude but I'm struggling with the angles.

Answer 1

R = (25 + 361 - 2·5·19cos(180° - 48°))^1/2 = 22.65 pounds (cosine law)

Angle α with 5 pounds force: 19/sinα = 22.65/sin132°; sinα = 19sin132°/22.65 = 0.6234; α = 38.564°; (sine law)

Angle β with force 19 pounds: β = 48° - 38.564° = 9.436°