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.

**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 cm
^{2} - B
,
266 cm
^{2} - C
,
485 cm
^{2} - D
,
341 cm
^{2}

**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.