Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Trigonometry - Cosine rule.
Test Yourself 1.

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Find a side	1. Find the length of the side marked x in the triangle at the right (answer to 2 decimal places): Answer.x = 12.58.
	2. Find the length of the side HJ in the triangle at the right (answer to 3 significant figures): Answer.HJ = 85.5.
	3. Find the value of the side marked x in the triangle at the right (answer correct to the nearest mm). Answer.x = 11.9 cm.
	4.
	6.
Find an angle.	7. Find the size of angle <FGH in the diagram at the right to the nearest degree. Answer.φ = 113°.
	8. A Qantas plane takes off from Sydney en route to Canberra. It is January and there are bushfires to the southnof Sydney in the Kangaroo Valley and Bungonia George. Hence the plane is diverted to fly via Yass. The diagram shows the distances between these three places. Through what angle (α) (to the nearest degree) must the pilot turn, while over Yass, to head towards Canberra? Answer.Angle of turn is 94°.
	9. Draw a triangle and mark the lengths of the sides as 5, 8 and 10. Find the size of the smallest angle (to the nearest minute).
	10.	The diagram to the left shows a quadrilateral ABCD. There is a right angle at angle C. The length of each side is indicated in red. (i) Find the length of BD (to the nearest whole number). (ii) Find the area of the quadrilateral. Answer.(i) BD = 64 (ii) .
	11. Three posts P, Q and R are placed such that PQ = 33m, QR = 45 m and RP = 51 m. Find the size of the angle at P subtended by QR to the nearest degree. Answer. Angle at P is 60°.
	12. In the diagram, AC is parallel to DB. AB = 6 cm. BC = 3 cm and AC = 7 cm. (i) Use the cosine rule to find the size of angle ACB to the nearest degree. (ii) Hence find the size of angle DBC giving reasons for your answer.
Practical problems.	13. David is playing golf on a hole which is 330 m long. He hits a good drive of 220 m but pulls it a little and the ball goes straight but to the left at an angle of 8°. How far is David's second shot to the hole?