The space diagram is shown in Figure (a).
(i) The horizontal component of the 5.0 N force,
oa = 5.0 cos 25° = 4.532,
and the vertical component of the 5.0 N force,
ab = 5.0 sin 25° = 2.113
(ii) The horizontal component of the 8.0 N force
oc = 8.0 cos 112° = −2.997
The vertical component of the 8.0 N force,
cd = 8.0 sin 112° = 7.417
(iii) Total horizontal component
= oa + oc = 4.532 + (−2.997)
= +1.535
(iv) Total vertical component
= ab + cd = 2.113 + 7.417
= +9.530
(v) The components are shown sketched in Figure (b).
By Pythagoras’ theorem,
and by trigonometry, angle
Hence the resultant of the two forces shown in Figure (a) is a force of 9.653 N acting at 80.85° to the horizontal.
