# Worksheet: Applications of Laws of Sines and Cosines

In this worksheet, we will practice deciding whether the rule of sines or the rule of cosines is most appropriate for solving a non-right triangle problem.

Q1:

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

Q2:

is a parallelogram where , and . Find the length of the diagonal giving the answer to two decimal places.

Q3:

is a parallelogram where and the diagonals and make angles of and respectively with the side . Find the length of the diagonals giving the answer to three decimal places.

• A ,
• B ,
• C ,
• D ,

Q4:

is a trapezium where , , and . Find giving the answer to the nearest minute.

• A
• B
• C
• D

Q5:

is a parallelogram where , the perimeter is 156 cm, the length of the small diagonal is 42 cm and . Find the area of the ABCD giving the answer to the nearest square centimetre.

Q6:

is a parallelogram where is the point of intersection to the diagonals, , and . Find the length of giving the answer to two decimal places.

Q7:

is a parallelogram where , and . Find the perimeter of giving the answer to two decimal places.

Q8:

is a parallelogram where , and . Find the perimeter of giving the answer to two decimal places.

Q9:

is a quadrilateral where , , , and . Find the lengths of and giving the answer to two decimal places.

• A ,
• B ,
• C ,
• D ,

Q10:

is a quadrilateral where , , , , and . Find the length of to the nearest centimetre and the area of to the nearest square centimetre.

• A , 467 cm2
• B , 266 cm2
• C , 485 cm2
• D , 341 cm2

Q11:

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

• A , ,
• B , ,
• C , ,
• D , ,

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 and the angle of elevation of the top of the office building is . Find, to the nearest metre, the distance between the top of the tower and the top of the office building.

Q13:

is a parallelogram where is the point of intersection to the diagonals, , and . Find the length of giving the answer to two decimal places.