Basic Trigonometry: Eduqas GCSE Higher November 2017 Paper 2 Q11

Higher November 2017 Paper 2 Q11

EduqasHigherCurrent spec6 marksBasic Trigonometry

11. A yacht set sail, at the start of its journey, on a bearing of 048°.
It sailed on this bearing for 3·8 km to Kew Rocks.
At Kew Rocks the yacht changed course and sailed to Dolphin Reach.

A triangle representing the yacht’s journey is shown below.
Some angles are given.

Start, Kew Rocks and Dolphin Reach form a triangle; Start to Kew Rocks is 3.8 km on a bearing of 48 degrees, the angle at Kew Rocks is a right angle, and the angle at Dolphin Reach is 54 degrees; North arrows at Start and Kew Rocks

Diagram not drawn to scale

(a) Find the bearing on which the yacht sailed from Kew Rocks to Dolphin Reach. [2]

(b) Calculate the distance the yacht would need to travel to go directly from Dolphin Reach back to the start.
Give your answer correct to 2 significant figures. [4]

Scheme	Marks	Comments
138(°)	B2	B1 for sight of an appropriate 48(°) and 42(°), or for 180(°) – 42(°) or 132(°) or 360(°) – 90(°) – 132(°)

Mark scheme (b)

Scheme	Marks	Comments
Start to Dolphin Reach \(= \dfrac{3.8}{\sin 54^\circ}\)	M2	M1 for \(\sin 54^\circ = 3.8/\text{distance}\)
4.7 (km)	A2	A1 for 4.697…(km) rounded or truncated (other than to 2 s.f. as required)
	(6)