An Eleven Plus Tangent

Years ago we used to use four figure tables when we were looking up tangents of an angle.

Angle A	Tan A	Angle A	Tan A
25	0.466 3	50	1.191 8
30	0.577 4	55	1.428 1
35	0.700 0	60	1.732 1
40	0.839 1	65	2.144 5
45	1.000 0	70	2.747 5

The angle of elevation of the top of a building is 25 degrees from a point 70 m away on level ground. Find the height of the building.

The Length is 70 m

The Height is x m

The height divided by the length = 0.4663 (We find this by looking at the table where the angle of 25 degrees = 0.466 3)

So the height = 0.4663 multiplied by the 70

The height of the building = 32.641 m

So when your eleven plus child appears to be going off at a tangent and not focussing on the task in hand:

The table he or she is working on may be in the wrong place or the wrong height or you may be looking at the wrong table.

The length of time you expect your child to work may be unrealistic

The tangent may be a realistic answer – especially if your child thinks in divergent forms.

You could, sensibly, ask your child to express 32.641 m to two significant figures – so the height of the building is 33 m. Easy when you know how!