Shape and Space 9

3 marks · Normal

In a solid with a rectangular base 7 cm × 10 cm, a point P is vertically above the centre of the base at a height of 12 cm. Explain how you would use trigonometry to find the angle between the edge from P to a base corner and the base plane.

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show mark scheme and worked solution

Marking points

M1 · 1 mark · States correct triangle: vertical and horizontal distances create a right triangle.

M2 · 1 mark · Identifies the angle is at P, between the slant edge and base projection.

A1 · 1 mark · Shows use of tangent: tan θ = vertical/horizontal, and mentions correct side lengths (half-diagonal for horizontal).

Worked solution

The edge from P to a base corner forms a right triangle with the vertical height (12 cm) and the horizontal distance from the centre to the corner.

Find the distance from the centre to a corner using Pythagoras:

Now use tan θ = vertical/horizontal = 12 / 6.10

This gives the angle between the edge and the base.