Question
In triangle ABC, AB = 45cm, AC = 29.5cm, BC = 35.3cm and angle CAB = 51.6°.
(i) Calculate angle ABC.
(ii) Calculate the area of triangle ABC.
The diagram shows a quadrilateral PQRS formed from two triangles, PQS and QRS.
Triangle PQS is isosceles, with PQ = PS = 32cm and angle SPQ = 56°.
QR = 47cm and angle SQR = 60°.
(i) Calculate SR.
(ii) Calculate the shortest distance from P to SQ.
Answer/Explanation
4(a)(i) 40.9 or 40.91…
4(a)(ii) 520 or 520.0 to 520.2…
4(b)(i) 41.2 or 41.21 to 41.23
4(b)(ii) 28.3 or 28.25 to 28.29…
Question
The diagram shows a field ABCDE.
(a) Calculate the perimeter of the field ABCDE.
m [4]
(b) Calculate angle ABD.
Angle ABD = [4]
(c) (i) Calculate angle CBD.
Angle CBD = [2]
(ii) The point C is due north of the point B.
Find the bearing of D from B.[2]
(d) Calculate the area of the field ABCDE.
Give your answer in hectares.
[1 hectare = 10 000m2]
hectares [4]
Answer/Explanation
Ans:
3(a) 530
3(b) 52.9 or 52.89…
3(c)(i) 28.1 or 28.07…
3(c)(ii) 331.9 or 331.9…
3(d) 1.5[0] or 1.498… nfww
Question
(a)
The diagram shows a toy boat. AC = 16.5 cm, AB = 19.5 cm and PR = 11 cm. Triangles ABC and PQR are similar.
(i) Calculate PQ.
(ii) Calculate BC.
(iii) Calculate angle ABC.
(iv) The toy boat is mathematically similar to a real boat. The length of the real boat is 32 times the length of the toy boat. The fuel tank in the toy boat holds 0.02 litres of diesel. Calculate how many litres of diesel the fuel tank of the real boat holds.
(b)
The diagram shows a field $D E F G$, in the shape of a quadrilateral, with a footpath along the diagonal $D F$. $D F=105 \mathrm{~m}$ and $F G=67 \mathrm{~m}$. Angle $E D F=70^{\circ}$, angle $E F D=32^{\circ}$ and angle $D F G=143^{\circ}$.
(i) Calculate $D G$.
(ii) Calculate EF.
▶️Answer/Explanation
(a) (i) 13 cao www
(ii) 10.39 to $10.4 \mathrm{wWW}$
(iii) 57.76 to 57.81 www
(iv) 655 to 655.4
(b) (i) 163.5 to $164 \mathrm{www}$
(ii) 100.8 to 100.9 or $101 \mathrm{www}$