# iGCSE Mathematics (0580) :E6.5 Solve simple trigonometrical problems in three dimensions including angle between a line and a plane.iGCSE Style Questions Paper 4

### Question

(a)
The diagram shows a quadrilateral PQRS formed from two triangles, PQS and QRS.
Calculate
(i) QR,
QR = …………………………………….. cm
(ii) PS,
PS = …………………………………….. cm
(iii) the area of quadrilateral PQRS.
…………………………………….$$cm^{2}$$
(b)
The diagram shows an open box ABCDEFGH in the shape of a cuboid.
AB = = 20 cm, BC 18 cm and AE = 16 cm.
A thin rod AGX rests partly in the box as shown.
The rod is 40cm long.
(i) Calculate GX, the length of the rod which is outside the box.
GX = …………………………………….. cm
(ii) Calculate the angle the rod makes with the base of the box.
………………………………………….

(a)(i) 2.67 or 2.666…
(ii) 4.14 or 4.140…
(iii) 20.4 or 20.35 to 20.36…
(b)(i) 8.7[0] or 8.695…
(ii) 30.7 or 30.73 to 30.74…

### Question

(b) Calculate DC.
DC = ……………………………………. cm
(c) Calculate the shortest distance from C to BD.
…………………………………….. cm

(a) 27[.0] or 26.97… n
(b) 9.19 or 9.192 to 9.193
(c) 6.15 or 6.149 to 6.151…

### 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

(a)$$BC^{2}=80^{2}+115^{2}-2\times 80\times 115\cos 72$$