(a) The diagram below shows a right-angled triangle.
Diagram not drawn to scale
Calculate the value of \(x\). [3]
\(x\) = ……………………
(b) The diagram below shows a different right-angled triangle.
Diagram not drawn to scale
Calculate the value of \(y\). [3]
\(y\) = ……………………
Mark scheme (a)
Scheme
Marks
Comments
(\(x\) =) 14·5 × sin 42
M2
Award M2 for 14·5 × cos 48 or \(\dfrac{14{\cdot}5 \times \sin 42}{\sin 90}\) M1 for \(\sin 42 = \dfrac{x}{14{\cdot}5}\) or \(\cos 48 = \dfrac{x}{14{\cdot}5}\) or \(\dfrac{x}{\sin 42} = \dfrac{14{\cdot}5}{\sin 90}\)
= 9·7(02….)
A1
Allow 10 from correct working. Award M2 A0 for an unsupported answer of –13·2895… (radians) or 8·88715…. (gradians).
Alternative method:
Scheme
Marks
Comments
Correct use of ‘two-step’ method.
M2
A partial trigonometric method is M0.
(\(x\)) = 9·7(02…)(cm)
A1
Accept an answer that rounds to 9·7(cm) Award M2 A0 for an answer of -13·2895… (radians) or 8·88715…. (gradians).
M1 for \(\cos y = \dfrac{13{\cdot}5}{15{\cdot}8}\) (= 0·854..)
Correct evaluation in the range 31·3 to 31·4
A1
Allow 31 from correct working. Allow correct angles given in radians (0·5463..) or gradians (34·7812….) Note: \(\cos y = 0{\cdot}85\) \(y = 31{\cdot}788\)… is awarded M2A0.
Alternative method:
Scheme
Marks
Comments
Correct use of ‘two-step’ method.
M2
A partial trigonometric method is M0.
Correct evaluation in the range 31·3 to 31·4
A1
Allow 31 from correct working. Allow correct angles given in radians (0·5463..) or gradians (34·7812….)
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