Answer:
Step-by-step explanation:
a) The Pythagorean theorem is used to find the length of the hypotenuse of a right triangle from the the lengths of the legs:
c² = a² + b²
c = √(a² + b²) = √(13.4² +9.54²) ≈ 16.45 . . . meters
____
b) Using an appropriate vector calculator, you can find the sum of the given forces to be ...
100∠140° +200∠70° +160∠250° = 119.733∠121.704°
The forces have a resultant equivalent to a force at 121.7°.
__
If you're calculating this by hand, you can add the components of the forces:
a∠b = (a·cos(b), a·sin(b))
100∠140° ≈ (-76.604, 64.279)
200∠70° ≈ (68.404, 187.939)
160∠250° ≈ (-54.723, -150.351)
(Values are shown rounded here. You never round intermediate calculations, but maintain full calculator precision until the final answer.) Then the sum of these forces is approximately ...
resultant ≈ (-62.924, 101.866)
The (second quadrant) angle of this resultant is ...
angle = arctan(101.866/-62.924) ≈ 121.7°
