Shape and Space 3
3 marks · NormalA straight road runs up a hill at a constant angle with the horizontal. The road makes an angle of 18° with the horizontal and is 120 m long.
Calculate the height gained, correct to 3 significant figures.
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37.0 m (±0.2)
Common mistakes: Using sin instead of tan; Not rounding to 3 significant figures
Show mark scheme and worked solution
Marking points
M1 · 1 mark · Selects correct approach: constructs right triangle and sets up h = 120 × tan(18°)
A1 · 1 mark · Correct use of tan(18°) and calculation of answer before rounding
A2 · 1 mark · Accurate answer given to 3 significant figures: 37.0 m
Worked solution
Let the height gained be h. The triangle formed has: