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Material Taken From:
Mathematics
for the international student
Mathematical Studies SL
Mal Coad, Glen Whiffen, John Owen, Robert Haese,
Sandra Haese and Mark Bruce
Haese and Haese Publications, 2004
Chapter 10 – Section C: Word Problems
Objectives
• To solve word problems using trigonometry.
• To find missing values in 3-dimensioinal
shapes.
1) Find the height of a tree which casts a shadow of 12.4
meters when the sun makes an angle of 52° to the horizon.
2) An A-frame house has the shape of an isosceles triangle
with base angles of 70. The oblique walls of the building are
12 meters long. How wide is the building at ground level?
Angles of Depression and Elevation
Angles of Depression and Elevation
3) From a vertical cliff 80 meters above sea level, a
fishing boat is observed at an angle of depression
of 6°. How far out to sea is the boat?
4) Find the angle of elevation from a bench to the
top of an 80 meter high building if the bench is 105
meters from the foot of the building.
5) The angle of depression from the roof of a building A
to the foot of a second building B across the same street
and 40 meters away is 65°. The angle of elevation of the
roof of building B to the roof of building A is 35°.
How tall is building B?
6) From a window, 29.6 meters above the ground,
the angle of elevation of the top of a building is
42°, while the angle of depression to the foot of the
building is 32°. Find the height of the building.
7) Ingrid measures the angle of elevation from a point
on level ground to the top of a building 120 meters
high to be 32°. She walks towards the building until
the angle of elevation is 45°. How far does she walk?
8) A builder designs a roof structure as illustrated.
The pitch of the roof is the angle that the roof makes
with the horizontal. Find the pitch of the roof.
Chapter 10 – Section E: 3-D Word Problems
9) A cube has sides of length 12 cm. Find the angle
between the diagonal AB and one of the edges at B.
10) Find the angle that:
a) PV makes with QV
b) SU makes with SQ
11) Find the angle between DG and the base plane EFGH.
12) The given figure shows a square-based pyramid
with apex directly above the center of its base.
The base is 10m by 10m and
its slant edges are 14 m long.
Find:
a) The length of MC
b) The angle that NC makes
with the base ABCD
13) A symmetric square-based pyramid has base
lengths of 6 cm and a height of 8 cm as shown.
Find the measure of:
a) angle TNM
b) angle TRM
Homework
• 10C, page 329
– #1, 5, 6, 9, 11, 14
• 10E.1, page 333
– #1, 3, 5
• 10E.3, page 336
– #2, 4, 5