Coplanar forces of magnitudes $58 \mathrm{N}, 31 \mathrm{N}$ and $26 \mathrm{N}$ act at a point in the directions shown in the diagram. Given that $\tan \alpha =\frac{5}{12},$ find the magnitude and direction of the resultant of the three forces.

A particle $P$ of mass $1.05 \mathrm{kg}$ is attached to one end of each of two light inextensible strings, of lengths $2.6 \mathrm{m}$ and $1.25 \mathrm{~m}$. The other ends of the strings are attached to fixed points $A$ and $B$, which are at the same horizontal level. $P$ hangs in equilibrium at a point $1 \mathrm{~m}$ below the level of $A$ and $B$ (see diagram). Find the tensions in the strings.

A block of mass $60 \mathrm{kg}$ is pulled up a hill in the line of greatest slope by a force of magnitude $50 \mathrm{N}$ acting at an angle $\alpha °$ above the hill. The block passes through points $A$ and $B$ with speeds $8.5 \mathrm{m}{ \mathrm{s}}^{-1}$ and $3.5 \mathrm{m}{ \mathrm{s}}^{-1}$ respectively (see diagram). The distance $AB$ is $250 \mathrm{m}$ and $B$ is $17.5 \mathrm{m}$ above the level of $A.$ The resistance to motion of the block is $6 \mathrm{N}.$ Find the value of $\alpha .$