find to the nearest tenth of a degree the angle formed bewteen the resultant force and smaller force?

Question

two forces of 50 pounds and 69 pounds act on a body to produce a resultant force of 70 pounds.

Answer 1

You're basically adding vectors here - you have a triangle where the sides are going to be 50, 69, and 70. You could try some vector addition to find the missing angle, but you could also use some old triangle formulas just the same.

Recall that in any triangle, you can relate the sides and an angle through

c^2 = a^2 + b^2 - 2abcosC

In our case, if we set a = 50, b = 70, and c = 69, the C would be the angle between a and b (naming conventions for triangles are that a side c is opposite an angle C - same name, just capitalization is different). So we can plug in and find that angle:

c^2 = a^2 + b^2 - 2abcosC
69^2 = 50^2 + 70^2 - 2(50)(70)(cosC)
4761 = 2500 + 4900 - 7000cosC
4761 = 7400 - 7000cosC
7000cosC = 2639
cosC = 0.377
C = 67.9