A 6.5 pole is to be supported by a wire extending from the top of the pole to the ground,making an angle of 22degrees to the vertical. How l

cos angle = adjacent (height of pole)/hypotenuse (length of wire, L) so

cos(22°) = 6.5/L  or L = 6.5/cos(22°)

$${\mathtt{L}} = {\frac{{\mathtt{6.5}}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{22}}^\circ\right)}}} \Rightarrow {\mathtt{L}} = {\mathtt{7.010\: \!475\: \!827\: \!402\: \!684\: \!9}}$$

L ≈ 7 m

if you can send the picture i will be able to help