review the graph. two forces of 25 pounds and 20 pounds act on a body with an angle of 25 degrees between…

Explanation:

Step1: Recall the law of cosines for vectors

If two - vectors $\vec{A}$ and $\vec{B}$ with magnitudes $A$ and $B$ and the angle $\theta$ between them, the magnitude $R$ of the resultant vector $\vec{R}=\vec{A}+\vec{B}$ is given by $R = \sqrt{A^{2}+B^{2}+2AB\cos\theta}$. Here, $A = 25$ pounds, $B = 20$ pounds, and $\theta=25^{\circ}$.

Step2: Substitute the values into the formula

First, calculate $A^{2}$, $B^{2}$, and $2AB\cos\theta$. $A^{2}=25^{2}=625$, $B^{2}=20^{2}=400$. $2AB\cos\theta=2\times25\times20\times\cos(25^{\circ})$. Since $\cos(25^{\circ})\approx0.9063$, then $2\times25\times20\times0.9063 = 906.3$.

Step3: Calculate the magnitude of the resultant force

$R=\sqrt{625 + 400+906.3}=\sqrt{1931.3}\approx43.95$ pounds.

Answer:

43.95 pounds