Area of any triangle and mixed trigonometry

3 exam-style questions. Answers and the mark for each step are on the last page.

Question 1Calculator · 2 marks
A triangle has sides of 8 cm and 11 cm with an angle of $47^\circ$ between them.
(a) Work out the area of the triangle. Give your answer correct to 3 significant figures. (2)
Question 2Non-calculator · 5 marks
A circle has radius 7 cm. A minor sector has angle 90 degrees.
(a) Find the exact area of the minor segment between its chord and arc. (3)
(b) Find the chord length exactly. (2)
Question 3Non-calculator · 3 marks
(a) A circle has centre O and radius 10 cm. Points A and B on the circle have minor angle AOB = $120^\circ.$ Work out the exact area of the minor segment bounded by chord AB and the minor arc AB. Give your answer in terms of $\pi$ and $\sqrt{3}.$ You must show your working. (3)

Answers and marks

(a) $32.2\text{ cm}^2$

(a) $\frac{49}{4}\pi -49/2$

(b) $7\sqrt{2}$

(a) $\frac{100\pi}{3} - 25\sqrt{3}$

P1 Establishing $\frac{120}{360}\pi \times 10^{2}$ or an equivalent valid method.
P1 Establishing $10\times 10\times \sin(120)/2$ or an equivalent valid method.
A1 Correct answer: $\frac{100\pi}{3} - 25\sqrt{3}$

Area of any triangle and mixed trigonometry

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