Question
The diagram shows the positions of three points A, B and C in a field.
(a) Show that BC is 118.1m, correct to 1 decimal place.
(b) Calculate angle ABC.
Angle ABC = …………………………………………
(c) The bearing of C from A is 147°.
Find the bearing of
(i) A from B,
………………………………………….
(ii) B from C.
………………………………………….
(d) Mitchell takes 35 seconds to run from A to C.
Calculate his average running speed in kilometres per hour.
…………………………………. km/h
(e) Calculate the shortest distance from point B to AC.
……………………………………… m
Answer/Explanation
(a)\( BC^{2}=80^{2}+115^{2}-2\times 80\times 115\cos 72\)
118.06…
(b) 67.8 or 67.9 or 67.83 to 67.88
(c)(i) 255
(c)(ii) [00]7.2
(d) 11.8 or 11.82 to 11.83
(e) 76.1 or 76.08 to 76.09
Question
In the diagram, BCD is a straight line and ABDE is a quadrilateral.
Angle BAC = 90°, angle ABC = 30° and angle CAE = 52°.
AC = 15.7cm, CE = 16.5cm and CD = 23.4cm.
(a) Calculate BC.
(b) Use the sine rule to calculate angle AEC.
Show that it rounds to 48.57°, correct to 2 decimal places.
(c) (i) Show that angle ECD = 40.6°, correct to 1 decimal place.
(ii) Calculate DE.
(d) Calculate the area of the quadrilateral ABDE.
Answer/Explanation
Answer:
(a) 31.4
(b) \([sinE=] \frac{15.7 \times sin 52}{16.5}\)
(c) (i) [∠ACE = ] 180 – 52 – 48.57
[= 79.43]
[∠ECD = ] 40.57…
(ii) 15.3 or 15.27 to 15.281 www
(d) 466 or 466.34 to 466.5