Question

Two donkeys are tied to the same pole.
One donkey pulls the pole at a strength of 6N
The other donkey pulls the pole at a strength of 3.5 in a direction that is 80° counterclockwise from the direction the first donkey is pulling towards. What is the combined strength of the donkeys' pulls?
Round your answer to the nearest tenth. You can round intermediate values to the nearest hundredth.

Answer 1

\[AD^2=AC^2+CD^2\]
\[\frac{ CD }{ BD}=\sin \alpha\]\[CD=BD \sin \alpha=Q \sin \alpha \]
\[\frac{ BC }{ BD }=\cos \alpha\]
\[BC=BD \cos \alpha=Q \cos \alpha\]
\[AD^2=(AB+BC)^2+(Q \sin \alpha)^2\]
\[AD^2=(P+Q \cos \alpha)^2+Q^2\sin^2 \alpha \]
\[=P^2+Q^2\cos^2 \alpha+2PQ \cos \alpha+Q^2\sin ^2 \alpha \]
if AD=R(resultant),then
\[R^2=P^2+Q^2+2PQ \cos \alpha \]
where alpha is the angle between two forces.
\[R^2=6^2+3.5^2+2\times 6\times 3.5 \cos 80\]
calculate and find the square root of R.