(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).
7. (a) 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: \(\cos y = 0{\cdot}85\) \(y = 31{\cdot}788\ldots\) is awarded M2A0.
7. (b) 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….)
We'd like to use Google Analytics cookies to count visits and see which pages help most. They're optional, and the site works exactly the same either way. Privacy policy
