IGCSE-H4-08e-01_3D_Trigonometry

For use only in the Aga Khan Academy
August 2012
IGCSE-H4-08e-01_3D_Trigonometry
3D Trigonometry
1.
In the pyramid ABCDE, the square base ABCD is horizontal and EM is vertical. M is the
midpoint of AC and N is the midpoint of AB. AB = 15cm and EM = 11cm.
(a) Find AM (to 3sf).
E
(b) Show that AE  15.3 cm (to 3sf).
(c) Calculate the angle ENM (to 1dp).
(d) Calculate
the angle (to 1dp)
between the line AE and the plane
ABCD.
D
C
M
A
2.
N
B
In the pyramid ABCDE, the rectangular base ABCD is horizontal and EM is vertical. M is
the midpoint of AC, N is the midpoint of BC and P is the midpoint of AD. AB = 15cm,
BC=20cm and EM = 12cm.
(a) Show that CM  12.5 cm
(b) Calculate
the angle (to 1dp)
E
between the line EC and the
horizontal base.
(c) Calculate the angle (to 1dp)
C
D
between the line EN and the
horizontal base.
(d) Calculate the angle NEP (to 1dp).
M
P
N
A
B
PTO
Copyright www.pgmaths.co.uk - For AS, A2 notes and IGCSE / GCSE worksheets
1
For use only in the Aga Khan Academy
3.
August 2012
IGCSE-H4-08e-01_3D_Trigonometry
In the pyramid ABCDE, the square base ABCD is horizontal and EM is vertical. M is the
midpoint of AC and N is the midpoint of AB. AB = 20cm and EM = 25cm.
(a) Show that BM  10 2 cm .
E
(b) Calculate
the angle (to 1dp)
between the line EB and the plane
ABCD.
(c) Find EB (to 3sf).
(d) Calculate the angle (to 1dp)
between the line EN and the
horizontal plane ABCD.
(e) Calculate the angle ABE (to 1dp).
D
(f) Calculate the length of AX (to 3sf)
C
where X is the point on EB such
that AX is perpendicular to EB.
M
(g) Calculate the angle AXC (to 1dp).
A
N
Copyright www.pgmaths.co.uk - For AS, A2 notes and IGCSE / GCSE worksheets
B
2

Download Report