Basic Trigonometry: WJEC GCSE Numeracy Higher June 2017 Unit 2 Q8

Numeracy Higher June 2017 Unit 2 Q8

WJECHigherCurrent spec6 marksBasic Trigonometry

8. The diagram below shows where Levi wants to attach a string of lights to his house.

A house with the string of lights along the two sloping edges of the front gable, from B up to the apex A and down to C

Levi wants to attach a single string of lights from B to A and then from A to C.
The diagram below shows the measurements Levi has taken.

Isosceles triangle ABC with AB = AC; a dashed perpendicular from A meets BC at a right angle, splitting BC into 2.5 m and 2.5 m; angle ACB is 52 degrees

Diagram not drawn to scale

He spends £410 at the electrical store buying a string of lights.
After putting up the lights, Levi finds he has 6 metres of the string of lights left over at one end.

How much did the electrical store charge Levi, per metre, for the string of lights? [6]

Mark scheme

Scheme	Marks	Comments
AB or AC = 2.5 ÷ cos52° OR AB or AC = 2.5 ÷ sin38° OR AB or AC = 4(.06067… m)	M2	M1 for any of the following cos52° = 2.5/ AB cos52° = 2.5/ AC sin38° = 2.5/AB sin38° = 2.5/AC equivalent full method without AB or AC as the subject
Total length 2 × 4(.06067…) (+ 6)	m1	FT ‘their derived AB or AC’ provided M1 awarded
14(.12… metres)	A1	FT from M1, m1 previously awarded
Cost per metre is 410 ÷ 14(.12…)	m1	FT from 'their total length' for m1 only Depends on previous M1
(£)29(.03…)	A1	CAO, i.e. (£)29.(….) (Note: 410 ÷14 = £29(.285…) Accept an answer that would round to (£)29 from correct working