# Worksheet: Applications on Sine and Cosine Laws

In this worksheet, we will practice using the cosine and sine law to solve real-world problems.

**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 triangle giving the answer to the nearest centimeter.

**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 centimeter.

**Q11: **

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

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

**Q12: **

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

**Q13: **

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

**Q14: **

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.

**Q15: **

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

**Q16: **

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

**Q17: **

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

**Q18: **

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.

**Q19: **

Find the area of the green part of the diagram, given that , , and . Give the answer to the nearest square centimeter.

**Q20: **

is an equilateral triangle inscribed in circle with a radius of 95 cm. Find the area of each shaded segment giving the answer to the nearest square centimeter.

**Q21: **

is a triangle where the ratio between , , and is and the radius of the circumcircle is 6 cm. Find the area of giving the answer to two decimal places.

**Q25: **

A man ran 24 km down a straight road. He then turned and ran a further 9 km along another straight road. Find, to the nearest kilometer, the shortest distance between his start and end points.