A wooden plank of the greatest possible length is placed in a garden shed. Use the diagram to calculate the length of the plank of wood correct to one decimal place.
Point $A$A is on a bearing of $15^\circ$15° from the base of a $80$80 m high tower with an angle of elevation of $22^\circ$22°. Point $B$B is on a bearing of $28^\circ$28° from the base of the tower with an angle of elevation of $8^\circ$8°.
A pyramid has a square base with side length $14$14 m and a vertical height of $24$24 m.
A tree stands at the corner of a square playing field. Each side of the square is $130$130 m long. At the centre of the field the tree subtends an angle of $22^\circ$22°.