The base of a flagpole is fixed to horizontal ground. It is held vertically by a straight rod of length 3·8 m. The rod is fixed to the ground and to a point 1·5 m from the top of the flagpole. The flagpole and the rod are shown in the diagram below.
Diagram not drawn to scale
Calculate the total height of the flagpole. Give your answer correct to the nearest centimetre. [4]
(b)
Mathematically similar large, medium and small flags are made.
Diagrams not drawn to scale
(i) Calculate the length of the medium flag. [2]
Length of the medium flag is …………… cm
(ii) Calculate the height of the small flag. [2]
Height of the small flag is …………… cm
Mark scheme (a)
Scheme
Marks
Comments
(Length of the flagpole below the rod =) 3.8 × sin 55° or 3.8 × cos (90° – 55°) or 380 × sin 55° or 380 × cos (90° – 55°)
M2
Or alternative full method M1 for correct working without isolating ‘length’ \(\sin 55^\circ\) = \(\dfrac{\text{length}}{3.8}\) or \(\cos (90^\circ - 55^\circ)\) = \(\dfrac{\text{length}}{3.8}\) or \(\sin 55^\circ\) = \(\dfrac{\text{length}}{380}\) or \(\cos (90^\circ - 55^\circ)\) = \(\dfrac{\text{length}}{380}\)
3.11(2…m) or 311(.2.. cm)
A1
Allow 3.1 (m) or 310 (cm)
(Total length 1.5 + 3.11 =) 4.61 (m) or 461 (cm)
A1
Must be to the nearest cm FT provided at least M1 previously awarded, i.e. for 1.5 + ‘their 3(.)11’ correctly evaluated, to nearest cm, and ‘their 3.11’ is to at least 2 decimal places
If units are given they must be correct
Mark scheme (b)
Scheme
Marks
Comments
(i) 120 × 64 ÷ 80 or 64 × 1.5 or 120 × 0.8 or 120 ÷ 1.25 or 64 ÷ \(\dfrac{2}{3}\) or equivalent
M1
96 (cm)
A1
Answer space takes precedence
(ii) 75 × 80 ÷ 120 or 75 ÷ 1.5 or 75 × \(\dfrac{2}{3}\) or 80 ÷ 1.6 or 80 × 0.625 or 64 × 75 ÷ 96 or equivalent
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