Two forces, A and B, have a resultant C. (In other words A + B = C, as vectors). If A = 5 N, B = 7 N and C = 8 N, what is the angle between A and C?

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Two forces, A and B, have a resultant C. (In other words A + B = C, as vectors). If A = 5 N, B = 7 N and C = 8 N, what is the angle between A and C?

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Answer 1 · 2018-05-14T16:06:36

$∠ B = \frac{π}{3} rad (60^{\circ})$ $angleB = pi/3" rad "(60^@)$

Explanation:

If we change the vectors to lower case and treat them as sides of a triangle, $a = 5, b = 7, and c = 8$ $a = 5, b = 7, and c = 8$ , then $∠ B$ $angle B$ is the angle between sides $a$ $a$ and $c$ $c$ ; this allows us to use the law of cosines:

$b^{2} = a^{2} + c^{2} - 2 (a) (c) cos (B)$ $b^2= a^2+c^2-2(a)(c)cos(B)$

$7^{2} = 5^{2} + 8^{2} - 2 (5) (8) cos (B)$ $7^2= 5^2+8^2-2(5)(8)cos(B)$

$7^{2} - 5^{2} - 8^{2} = - 2 (5) (8) cos (B)$ $7^2-5^2-8^2=-2(5)(8)cos(B)$

$cos (B) = \frac{7^{2} - 5^{2} - 8^{2}}{- 2 (5) (8)}$ $cos(B)=(7^2-5^2-8^2)/(-2(5)(8))$

$cos (B) = \frac{1}{2}$ $cos(B)=1/2$

$∠ B = \frac{π}{3} rad$ $angleB = pi/3" rad"$

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Two forces, A and B, have a resultant C. (In other words A + B = C, as vectors). If A = 5 N, B = 7 N and C = 8 N, what is the angle between A and C?

1 Answer

Explanation:

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