Basic Trigonometry: WJEC GCSE Numeracy Intermediate June 2017 Unit 2 Q12

Numeracy Intermediate June 2017 Unit 2 Q12

WJECIntermediateCurrent spec4 marksBasic Trigonometry

12. Ursula is lying on her surfboard 180 metres away from the foot of a vertical cliff.
The height of the cliff is 146 metres.

Right-angled diagram: Surfboard on a horizontal line 180 m from the foot of a vertical cliff of height 146 m

Diagram not drawn to scale

Ursula was told that if the angle of elevation of the top of the cliff from her lying position is between 42° and 45°, it is safe for her to attempt to stand on her surfboard.

Calculate the angle of elevation of the top of the cliff from Ursula’s position lying on her surfboard.

State whether it is

safe for Ursula to attempt to stand, or
not safe as she is too near the cliff, or
not safe as she is too far out at sea. [4]

Mark scheme

Scheme	Marks	Comments
tan^-1 0.81(1…) or tan^-1 146/180 Angle of elevation is 39.(04…°)	M2 A1	M1 for tan (angle of elevation) = 146/180
Statement e.g. ‘(not safe as) too far (from the foot of the cliff)’, ‘too far out at sea’	E1	FT ‘their acute angle’ provided at least M1 previously awarded, with <42° being too far out, or >45° too near the cliff, or between these angles it is safe Alternative for M marks, e.g.: sin (elevation) = \(\dfrac{146}{\sqrt{(180^2 + 146^2)}}\) ( = \(\dfrac{146}{231.767..}\)) OR cos (elevation) = \(\dfrac{180}{\sqrt{(180^2 + 146^2)}}\) M1 sin^-1 0.62994.... OR cos^-1 0.7766... M1 If no marks: Award SC1 for an answer of 50.95…° or 51° AND ‘too near’