Basic Trigonometry: WJEC GCSE Higher November 2017 Unit 2 Q7

Higher November 2017 Unit 2 Q7

WJECHigherCurrent spec6 marksBasic Trigonometry

7. The diagram shows two right-angled triangles, joined together along a common side.
\(S\hat{P}Q\) = 90°, \(S\hat{Q}R\) = 90°, \(S\hat{Q}P\) = 38°, \(PS\) = 8 cm and \(QR\) = 15 cm.

Right-angled triangle SPQ with the right angle at P, PS = 8 cm and angle SQP = 38 degrees, joined along SQ to right-angled triangle SQR with the right angle at Q, QR = 15 cm and angle x at S

Diagram not drawn to scale

Calculate the size of angle \(x\). [6]

Mark scheme

Scheme	Marks	Comments
QS = \(\dfrac{8}{\sin 38}\)	M2	M1 for \(\dfrac{8}{\text{QS}} = \sin 38\). Accept M1 for \(\dfrac{\text{QS}}{\sin 90} = \dfrac{8}{\sin 38}\) M2 for QS = \(\dfrac{8 \times \sin 90}{\sin 38}\)
= 13 or 12·99(..)	A1
tan x = \(\dfrac{15}{12.99(..)}\)	M1	F.T. ‘their 12.99(..)’, stated or shown on diagram.
x = tan⁻¹ (15/12·99…)	m1
= 49(·098..°)	A1	Mark final answer. If FT leads to a non-integer value, allow to the nearest degree.