O-LevelMathematicsTrigonometry4024/22 · Oct/Nov 2022 · Q78 Marks
[Figure of irregular quadrilateral ABCD with sides 95, 107, 165, 160 and angle at A 90 degrees] ABCD is the floor plan of an exhibition hall with dimensions shown in metres. Points A, B, C and D all lie on the same horizontal plane.
- (a)Calculate angle BCD.[4]
- (b)A light is attached to the ceiling vertically above B. The angle of elevation of the light from C is 8.2°. Calculate the angle of elevation of the light from A.[4]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.
- [4] M1 for 160² + 95² oe M2 for [cos =] (107² +165² – their34625) / (2×107×165) oe or M1 for (their34625)= 107² +165²-2×107×165×cos[] oe
- [4] M2 for 107 tan 8.2 or 107/tan 81.8 or 107sin 8.2/sin 81.8 oe or M1 for tan 8.2 = height/107 or tan 81.8 = height/107 or sin 8.2 = height/sin 81.8 oe M1 for tan [ ] = theirheight/95 oe
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