A fridge of height 2m and width 0.8m is tilted in a delivery van so that one edge rests on the edge of a table and another touches the ceiling, as shown in the diagram. The total height of the inside of the van is 1.5m. Find the height of the table.

Let h be the height of the table. Let the edges of the fridge be A touching the ceiling, B touching the table and C touching the floor. Let D be the point on the ceiling vertically above B and E be the point where the table leg meets the floor (Draw all this out in a 2D diagram). Then we have two triangles with the following information: ACD has sides AB of 0.8m and BD of (1.5-h)m, and BCE has sides BC of 2m and BE of (h)m. Looking at the right angles, angles on a straight line and angles in a triangle, we see the angle equals 90- and =90-=. Therefore the two triangles are similar so corresponding sides are in proportion. We have then that h/2=AD/0.8, so AD=0.4h.

By Pythagoras Theorem on the right angled triangle ABD, we obtain the quadratic equation in h: 0.8^2 = (0.4h)^2 + (1.5-h)^2 which expands and simplifies to 1.16h^2 - 3h + 1.61 = 0. We can solve this using the quadratic formula and end up with two possible answers, 1.83 and 0.76. Since the height of the van is 1.5m, the table cannot be 1.83m tall so the answer must be 0.76m.