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 H: The Sine Rule
Solving Triangles
• To solve a non-right triangle you need at
least 3 pieces of information:
– 3 sides SSS
– 2 sides & the angle between
– 2 sides & an angle opposite
– 2 angles & 1 side ASA, AAS
SAS
SSA
Sine Rule
a
b
c


sin A sin B sin C
SSA
ASA, AAS
C
a
b
A
c
B
1) Find the length of AC.
2) Find the length of AB.
3) In the diagram, triangle ABC is isosceles. AB =
AC, CB = 15 cm and angle ACB is 23°.
Find:
(a) the size of angle CAB;
(b) the length of AB.
A
C
23º
15 cm
Diagram not to scale
B
4) A farmer wants to construct a new fence
across a field. The plan is shown below.
The new fence is indicated by a dotted
line. Calculate the length of the fence.
75°
40°
410 m
Diagram not to scale
5) The figure shows a triangular area in a park surrounded by
the paths AB, BC and CA, where AB = 400 m.
(a) Find the length of AC using the above information.
Diana goes along these three paths in the park at an average
speed of 1.8 m/s.
(b) Given that BC = 788m, calculate how many minutes she
takes to walk once around the park.
diagram not to scale
A
400 m
30º
B
C
6) In triangle ABC, AC = 5, BC = 7, A = 48°, as
shown in the diagram
Find the measure of angle ABC giving your
answer correct to the nearest degree.
C
7
5
A
48°
diagram not to scale
B
7) The diagram below shows triangle PQR. The
length of [PQ] is 7 cm, the length of [PR] is 10 cm,
and PQR is 75°.
(a) Find PRQ
(b) Find the area of triangle PQR
diagram not to scale
Homework
• Worksheet
–#1abef
–#2a
–#3ace
• Pg 341 – H.1 2abc