Shape and Space 9

2 marks · Normal

For a square-based pyramid with base edge of 10 cm and height of 15 cm (vertex directly above the centre), work out the vertical angle (angle between a side face and the base).

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.

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56.3° degrees (±0.1)

Also accept: 56.31°; 56°18′

Common mistakes: Using base length instead of half for the triangle base.

Show mark scheme and worked solution

Marking points

M1 · 1 mark · Sets up correct triangle and uses tan or trig to find the angle.

A1 · 1 mark · Gives answer 56.3° (1 dp) or equivalent. (follow-through)

Worked solution

The right triangle from centre to face base midpoint to vertex has base 5 cm (half of 10 cm) and height 15 cm.

However, the angle between the base and side face: consider slant height. The slant height is cm.