# Worksheet: Applications of Laws of Sines and Cosines

In this worksheet, we will practice solving triangles using the sine law, the cosine law, or both of them.

**Q1: **

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

**Q2: **

is the midpoint of and . Find giving the answer to three decimal places.

**Q3: **

is a triangle where . Find the largest angle in giving the answer to the nearest degree.

**Q4: **

is a triangle where , and . Point lies on such that . Find the length of giving the answer to two decimal places.

**Q5: **

is a triangle, where cm, cm, and . Find the radius of the circumcircle giving the answer to two decimal places.

**Q6: **

is a triangle where cm, cm and cm. Find the radius of the circumcircle giving the answer to three decimal places.

**Q7: **

is a triangle where ,
the ratio between and is and the area of the circumcircle is cm^{2}.
Find the perimeter of the triangle giving the answer to the nearest centimetre.

**Q8: **

is a quadrilateral where , , , and . Find giving the answer to the nearest second and the area of giving the answer to three decimal places.

- A
,
88.123 cm
^{2} - B
,
37.767 cm
^{2} - C
,
134.283 cm
^{2} - D
,
67.142 cm
^{2}

**Q9: **

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

**Q10: **

Find the area of given is the point of intersection of and , , , , and . Give the answer to the nearest square centimetre.

**Q11: **

is a right-angled triangle at where and . Find the length of to two decimal places and then the measure of angles and to the nearest second.

- A , ,
- B , ,
- C , ,
- D , ,

**Q12: **

is a right-angled triangle at where and . Find the lengths of and giving the answer to two decimal places and the measure of giving the answer to the nearest degree.

- A , ,
- B , ,
- C , ,
- D , ,

**Q13: **

is a right-angled triangle at where and . Find the lengths and giving the answer to two decimal places and the measure of angle giving the answer to the nearest degree.

- A , ,
- B , ,
- C , ,
- D , ,

**Q14: **

is a right-angled triangle at where and . Find in radians and lengths and giving all answers to three decimal places.

- A , ,
- B , ,
- C , ,
- D , ,

**Q15: **

is a right-angled triangle at where and . Find in radians and the lengths and giving all answers to three decimal places.

- A , ,
- B , ,
- C , ,
- D , ,

**Q16: **

is an isosceles triangle where and . Find the angles in the triangle giving the answer to the nearest second.

- A
- B
- C
- D

**Q17: **

is a trapezium, where , , , , and . Find the lengths of and giving the answer to the nearest centimetre.

- A ,
- B ,
- C ,
- D ,
- E ,

**Q18: **

is a trapezium where , , , and . Find the area of the trapezium giving the answer to the nearest square centimetre.

**Q19: **

is a trapezium, where , , , , and . Find the area of the trapezium giving the answer to the nearest square centimetre.

**Q20: **

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

**Q21: **

is a triangle where ,
and the area of the triangle is cm^{2}.
Find the perimeter of giving the answer to two decimal places.

**Q22: **

In a parallelogram , and , where . Work out the length of . Give your answer to 2 decimal places.

**Q23: **

The side length of a regular pentagon is 25.81 cm. Find the length of the diagonal giving the answer to two decimal places.

**Q24: **

In a triangle , , , and .

If is the altitude from , what is to 2 decimal places?

Calculate the area of the triangle to 2 decimal places.