Find-the-magnitude-of-two-forces-such-that-if-they-act-at-right-angle-their-resultant-is-10-and-13-if-they-act-at-an-angle-of-60-

Question Number 11405 by tawa last updated on 24/Mar/17

Find the magnitude of two forces such that if they act at right angle their

resultant is \sqrt{10}, and \sqrt{13} if they act at an angle of 60 ° .

Answered by mrW1 last updated on 24/Mar/17

x^{2} + y^{2} = 10

{(y + x \cos 60 °)}^{2} + {(x \sin 60 °)}^{2} = 13

{(y + \frac{1}{2} x)}^{2} + {(\frac{\sqrt{3}}{2} x)}^{2} = 13

y^{2} + \frac{1}{4} x^{2} + x y + \frac{3}{4} x^{2} = 13

x^{2} + y^{2} + x y = 13

x y = 3

2 x y = 6

{(x + y)}^{2} = 16

x + y = 4

{(x - y)}^{2} = 4

x - y = 2

2 x = 6

x = 3

y = 1

Commented by tawa last updated on 24/Mar/17

God bless you sir .

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