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In this lesson, we will learn how to decide whether the rule of sines or the rule of cosines is most appropriate for solving a non-right triangle problem.

Q1:

π is a circle with radius 24 cm. A chord is drawn whose central angle is 6 2 β . Find the length of the chord giving the answer to the nearest cm.

Q2:

π΄ π΅ πΆ π· is a parallelogram where π΄ π΅ = 1 0 . 2 c m , π β πΆ π΄ π΅ = 3 4 1 8 β² β and π β π· π΅ π΄ = 6 3 1 2 β² β . Find the length of the diagonal π΄ πΆ giving the answer to two decimal places.

Q3:

π΄ π΅ πΆ π· is a parallelogram where π΄ π΅ = 4 . 3 c m and the diagonals π΄ πΆ and π΅ π· make angles of 4 9 β and 9 4 β respectively with the side π΄ π΅ . Find the length of the diagonals giving the answer to three decimal places.

Q4:

π΄ π΅ πΆ π· is a trapezium where π΄ π· β₯ πΆ π΅ , π΄ π· = 4 c m , π΄ π΅ = 1 7 c m and π β π΅ π΄ π· = 1 0 8 β . Find π β π· π΅ πΆ giving the answer to the nearest minute.

Q5:

π΄ π΅ πΆ π· is a parallelogram where π β π΄ = 6 0 β , the perimeter is 156 cm, the length of the small diagonal is 42 cm and π΄ π΅ < π΄ π· . Find the area of the ABCD giving the answer to the nearest square centimetre.

Q6:

π΄ π΅ πΆ π· is a parallelogram where π is the point of intersection to the diagonals, π΄ πΆ = 1 8 c m , π β π΄ π π· = 9 0 6 β² β and π β πΆ π΄ π΅ = 3 5 1 2 β² β . Find the length of π΅ π· giving the answer to two decimal places.

Q7:

π΄ π΅ πΆ π· is a parallelogram where π β π΄ = 7 9 4 2 β² β , π β π· π΅ πΆ = 6 8 4 2 β² β and π΅ π· = 3 2 . 3 c m . Find the perimeter of π΄ π΅ πΆ π· giving the answer to two decimal places.

Q8:

π΄ π΅ πΆ π· is a parallelogram where π β π΅ = 1 1 4 β , π β π· π΅ πΆ = 5 5 β and π΅ π· = 2 2 c m . Find the perimeter of π΄ π΅ πΆ π· giving the answer to two decimal places.

Q9:

π΄ π΅ πΆ π· is a quadrilateral where π΄ π΅ = 1 4 c m , π΅ πΆ = 2 8 c m , β π΄ π΅ πΆ = 9 0 β , β π΅ πΆ π· = 6 9 β and β πΆ π· π΄ = 8 4 β . Find the lengths of π΄ π· and πΆ π· giving the answer to two decimal places.

Q10:

π΄ π΅ πΆ π· is a quadrilateral where π΄ π΅ = 2 4 c m , π΅ πΆ = 1 8 c m , πΆ π· = 9 c m , π΄ πΆ = 3 0 c m , and π β π΄ πΆ π· = 6 8 1 2 β² β . Find the length of π΄ π· to the nearest centimetre and the area of π΄ π΅ πΆ π· to the nearest square centimetre.

Q11:

The side length of a regular octagon is 39.7 cm. Find the length of the diagonals π» π΅ , π» πΆ , and π» π· , giving your answer to three decimal places.

Q12:

The height of a tower is 139 m and the height of an office building is 54 m. From a point on level ground between them, the angle of elevation of the top of the tower is 6 8 β and the angle of elevation of the top of the office building is 4 8 β . Find, to the nearest metre, the distance between the top of the tower and the top of the office building.

Q13:

π΄ π΅ πΆ π· is a parallelogram where π is the point of intersection to the diagonals, π΄ πΆ = 2 0 . 5 c m , π β π΄ π π· = 1 4 2 β and π β πΆ π΄ π΅ = 6 5 4 8 β² β . Find the length of π΅ π· giving the answer to two decimal places.

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