# 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 cm2. 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 cm2
• B , 37.767 cm2
• C , 134.283 cm2
• D , 67.142 cm2

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 cm2. 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.

Q22:

Two planes leave the same airport at the same time. One flies on a bearing of at 500 miles per hour. The other flies on a bearing of at 600 miles per hour. How far apart are the planes after 2 hours?

Q23:

The shown diagram represents a satellite calculating the distances and the angle. Find the distance between the two cities. Give your answer to one decimal place. Note that the diagram is not to scale.

Q24:

A 113-foot tower is located on a hill that is inclined to the horizontal, as shown in the figure. A guy wire is to be attached to the top of the tower and anchored at a point 98 feet uphill from the base of the tower. Find the length of wire needed.

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.