two forces of 409 newtons and 512 newtons act on a point. the resultant force is 888 newtons. find the angle…

two forces of 409 newtons and 512 newtons act on a point. the resultant force is 888 newtons. find the angle between the two forces.\nthe angle between the two forces is (square^{circ}).\n(round to the nearest integer as needed.)

two forces of 409 newtons and 512 newtons act on a point. the resultant force is 888 newtons. find the angle between the two forces.\nthe angle between the two forces is (square^{circ}).\n(round to the nearest integer as needed.)

Answer

Explanation:

Step1: Use resultant - force formula

Let the two forces be $F_1 = 409$, $F_2 = 512$ and the resultant force $R = 888$. The formula for the magnitude of the resultant of two forces is $R^{2}=F_1^{2}+F_2^{2}+2F_1F_2\cos\theta$. So, $888^{2}=409^{2}+512^{2}+2\times409\times512\times\cos\theta$.

Step2: Solve for $\cos\theta$

$788544 = 167281+262144 + 420352\cos\theta$. $788544-(167281 + 262144)=420352\cos\theta$. $359119 = 420352\cos\theta$. $\cos\theta=\frac{359119}{420352}\approx0.8543$.

Step3: Find $\theta$

$\theta=\cos^{- 1}(0.8543)\approx31^{\circ}$.

Answer:

$31$