1. 3. Non-Right Triangles: Cosine Law & Area
Questions to try:
Pearson Ch 7, p238
(pdf on Moodle)
Q17, 18, 19, 22
p248 Q13
p249 Q14 & 16

2. The Cosine Law
Use cosine law to solve a non-right triangle when:

3. Examples to Try
1. Solve the following triangles. Give all sides to one decimal place and all angles to the nearest degree.
2. A cyclist rode her bicycle for 22km on a straight road heading in a westerly direction towards a junction. At the junction, she headed down another straight road bearing 200° for a distance of 15km. How far is the cyclist from her starting position?

4. Area of a Triangle Recall: formula for area of a triangle: A = ½ bh
To calculate height:
So for ANY triangle, where we know two sides and the contained angle, we can calculate area of a triangle:
3. The diagram shows a triangular children’s playground. Find the area of the playground.

5. Examples to Try
Find the area of the triangle PQR given that PQ = 9 cm, QR = 10 cm
and ∠PQR = 40°.
The diagram shows the triangle ABC, which has an area of 10 cm2.
Find ∠ACB, given that it is an obtuse angle.
Find AB.

8. A triangular sandpit having side lengths 5m, 4m and 8m is to be constructed to a depth of 20 cm. Find the volume of sand needed to fill this sandpit.
The diagram shows triangle PQR, with ∠Q = 118°, PQ = 9.5 m, and QR = 11.5 m.
Find PR
Find ∠P