Solving triangles that are not right-angled with the sine and cosine rules, the area formula ½ab sin C, the area of a segment, and bearing problems.
6 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.
A ship sails 12 km on one bearing and then 9 km on another. How far is it from the start, and on what bearing? Sine, cosine and a compass give the answer.
Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.
Change the bearing; solve triangles.
Copy these into your notebook in your own words — that is how they stick.
Side a opposite angle A, etc.
a/sin A = b/sin B = c/sin C. Two angles + a side; or two sides + a non-included angle (ambiguous case).
a² = b² + c² − 2bc cos A. Two sides + included angle, or three sides: cos A = (b² + c² − a²)/2bc.
½ab sin C (C between a and b).
Sector − triangle: θ/360 × πr² − ½r² sin θ.
Clockwise from North, 3 figures. Back bearing ± 180°. Draw a North line at each point.
Right-angled: Pythagoras/SOH CAH TOA. Otherwise: pair (side, opposite angle) known → sine rule; two sides + included angle or three sides → cosine rule.
Largest side opposite the largest angle; angles add to 180°.
3 quick games on this lesson. Earn XP and badges as you play — your best score for each game is saved. Games are for practice and do not change your exam readiness. More games in the Mathematics Arcade.
8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.
Write full answers, then reveal the mark scheme and tick the points you earned (19 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [10 marks]
A ship sails from A to B, a distance of 12 km on a bearing of 060°. It then sails 9 km to C on a bearing of 150°.
(a) Draw a sketch showing the journey with North lines and the bearings marked. (Check: North line at A and B, 060° from North at A, 150° from North at B.) [3]
(b) Show that angle ABC = 90°. [2]
(c) Calculate the distance AC. [2]
(d) Calculate the bearing of C from A, to the nearest degree. [3]
Question 2 [9 marks]
In triangle ABC, AB = 8 cm, AC = 11 cm and angle BAC = 57°.
(a) Calculate the length of BC, to 3 significant figures. [4]
(b) Calculate the area of the triangle. [2]
(c) A circle of radius 8 cm has a chord that subtends an angle of 90° at the centre. Calculate the area of the segment cut off by the chord. [3]
Find these in your own past-paper booklets for extra timed practice. Items above are written in the style of these papers; any adapted from a specific question say so.