use the parallelogram rule to find the magnitude of the resultant force for the two forces shown in the…

Explanation:

Step1: Recall the law of cosines for resultant force

If two forces $F_1$ and $F_2$ act at an angle $\theta$ to each other, the magnitude of the resultant force $R$ is given by $R=\sqrt{F_1^{2}+F_2^{2}-2F_1F_2\cos(180 - \theta)}$. Here $F_1 = 27$ lb, $F_2=29$ lb and $\theta = 134^{\circ}$. Since $\cos(180 - \alpha)=-\cos\alpha$, the formula becomes $R=\sqrt{F_1^{2}+F_2^{2}+2F_1F_2\cos\theta}$.

Step2: Substitute the values

Substitute $F_1 = 27$, $F_2 = 29$ and $\theta=134^{\circ}$ into the formula. $R=\sqrt{27^{2}+29^{2}+2\times27\times29\times\cos(134^{\circ})}$. First, calculate the squares and the product - cosine term: $27^{2}=729$, $29^{2}=841$, and $2\times27\times29\times\cos(134^{\circ})=2\times27\times29\times(- 0.71934)=2\times27\times29\times(-0.71934)\approx - 1143.7$. Then $R=\sqrt{729 + 841-1143.7}=\sqrt{1570 - 1143.7}=\sqrt{426.3}$.

Step3: Calculate the square - root and round

$\sqrt{426.3}\approx20.6$.

Answer:

$20.6$