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9 exam-style questions with model answers, plus 12 quick multi-choice questions — every question on the site for this standard, grouped by the 3 pages of notes they come from.
Write a full answer before you reveal the model one — that comparison is where the marks come from. Every block links back to the notes that teach it.
In triangle , , and cm. Find the length of side .
A surveyor stands at point and measures the angle to a tree at as 63° from the line . From point , 85 m from , the angle to the tree is 47° from the line . Find the distance from to the tree.
In triangle , , cm and cm. Determine, with reasoning, the values of for which there are (i) no triangles, (ii) exactly one triangle, and (iii) two triangles.
In triangle , cm, cm and the angle at is . Find the length of .
A triangular garden bed has sides of 6.5 m, 8.2 m and 11.4 m. Find its largest angle and its area.
A ship sails 45 km on a bearing of 062°, then changes course and sails 70 km on a bearing of 145°. Find the ship's distance and bearing from its starting point, and the shortest distance it came to a lighthouse that lies 30 km due east of the starting point.
A sector of a circle has radius 9 cm and a centre angle of . Find the arc length and the sector area.
A fan-shaped window is a sector with an area of 2.4 m2 and a radius of 1.8 m. Find the angle at the centre and the total length of framing needed around the window.
A goat is tethered by a 6 m rope to the corner of a rectangular barn measuring 4 m by 10 m, on the outside. Find the total grazing area available to the goat.