Temi’s sailing boat has a sail in the shape of a right-angled triangle, \({\text{ABC}}{\text{.}}\,\,\,{\text{BC}} = \,\,5.45{\text{m}}\),
angle \({\text{CAB}} = {76^{\text{o}}}\) and angle \({\text{ABC}} = {90^{\text{o}}}\).

Calculate \({\text{AC}}\), the height of Temi’s sail.

William also has a sailing boat with a sail in the shape of a right-angled triangle, \({\text{TRS}}\).
\({\text{RS}}\,\,{\text{ = }}\,\,{\text{2}}{\text{.80m}}\). The area of William’s sail is \({\text{10}}{\text{.7}}\,{{\text{m}}^2}\).

Calculate \({\text{RT}}\), the height of William’s sail.

Units are required in parts (a) and (b).

\({\text{sin}}\,\,{76^{\text{o}}} = \,\,\frac{{5.45}}{{{\text{AC}}}}\)        (M1)

Note: Award (M1) for correct substitution into correct trig formula. 

\({\text{AC}}\,\, = \,\,5.62{\text{m}}\,\,\,( = 5.61684...{\text{m}})\)        (A1) (C2)

Note: The answer is \(5.62{\text{m}}\), the units are required. 

[2 marks]

\(\frac{1}{2}\,\, \times \,\,2.80\,\, \times \,\,{\text{RT}}\,\,{\text{ = }}\,\,{\text{10}}{\text{.7}}\)        (M1)

Note: Award (M1) for correct substitution into area of a triangle formula or equivalent.

\({\text{RT}}\,\,{\text{ = }}\,\,{\text{7}}{\text{.64}}\,{\text{m   (7}}{\text{.64285}}...{\text{m)}}\)        (A1) (C2)

Note: The answer is \({\text{7}}{\text{.64}}\,{\text{m}}\), the units are required.

[2 marks]

Question 2: Trigonometry and area
The response to this question was mixed, with many fully correct attempts. Those failing to score 6 marks often either lost a mark due to the use of Pythagoras and premature rounding or due to an incorrect trigonometric ratio used in a right angled triangle. The use of sine and cosine rule often led to errors.

Question 2: Trigonometry and area
The response to this question was mixed, with many fully correct attempts. Those failing to score 6 marks often either lost a mark due to the use of Pythagoras and premature rounding or due to an incorrect trigonometric ratio used in a right angled triangle. The use of sine and cosine rule often led to errors.