3. Non-Right Triangles: Cosine Law & Area

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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

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

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?

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.

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.

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