# Lesson Worksheet: Applications on Sine and Cosine Laws Mathematics

In this worksheet, we will practice using the laws of sines and cosines to solve real-world problems.

Q1:

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

Q2:

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

Q3:

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.

Q4:

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

Q5:

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

Q6:

Find the area of given is the point of intersection of and , , , , and . Give the answer to the nearest square centimeter. Q7:

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.

Q8:

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

Q9:

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

Q10:

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.

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