Material Taken From:

Mathematicsfor the international student

Mathematical Studies SL

Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark Bruce

Haese and Haese Publications, 2004

Solving Triangles

• To solve a non-right triangle you need at least 3 pieces of information:–3 sides–2 sides & the angle between–2 sides & an angle opposite–2 angles & 1 side

SAS

ASA, AAS

SSS

SSA

Chapter 10 – Section H: The Sine Rule

Sine Rule

a

A

b

B

c

Csin sin sin

A

C

B

ab

c

ASA, AAS

SSA

1) Find the length of AC.

2) Find the length of AB.

Find:(a) the size of angle CAB;(b) the length of AB.

Diagram not to scale

3) In the diagram, triangle ABC is isosceles. AB = AC, CB = 15 cm and angle ACB is 23°.

A

C B23º15 cm

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 mDiagram not to scale

A

B

C

4 0 0 m

3 0 º

d iag ram n o t to sca le

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.

Find the measure of angle ABC giving your answer correct to the nearest degree.

6) In triangle ABC, AC = 5, BC = 7, A = 48°, as shown in the diagram

A B

C

5 7

48°

diagram not to scale

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