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:

𝐴𝐵𝐶 is a triangle, where 𝑎=19 cm, 𝑏=9 cm, and 𝑚𝐶=45. Find the radius of the circumcircle giving the answer to two decimal places.

Q2:

𝐴𝐵𝐶 is a triangle where 𝑎=26 cm, 𝑏=22 cm and 𝑐=6 cm. Find the radius of the circumcircle giving the answer to three decimal places.

Q3:

𝐴𝐵𝐶 is a triangle where 𝑚𝐴=30, the ratio between 𝑏 and 𝑐 is 32, and the area of the circumcircle is 225𝜋 cm2. Find the perimeter of triangle 𝐴𝐵𝐶 giving the answer to the nearest centimeter.

Q4:

𝐴𝐵𝐶𝐷 is a quadrilateral where 𝐴𝐵=16cm, 𝑚𝐴𝐷𝐵=40, 𝑚𝐷𝐵𝐴=100, 𝐵𝐶=21cm and 𝐷𝐶=9cm. Find 𝑚𝐵𝐶𝐷 giving the answer to the nearest second and the area of 𝐵𝐶𝐷 giving the answer to three decimal places.

  • A111106, 88.123 cm2
  • B233323, 37.767 cm2
  • C692358, 134.283 cm2
  • D451630, 67.142 cm2

Q5:

𝐴𝐵𝐶𝐷 is a quadrilateral where 𝑚𝐴𝐵𝐶=90, 𝑚𝐵𝐴𝐷=41, 𝐴𝐵=𝐴𝐷=30.9cm and 𝐵𝐷=𝐵𝐶. Find the area of 𝐴𝐵𝐶𝐷 giving the answer to two decimal places.

Q6:

Find the area of 𝐴𝐵𝐶𝐷 given 𝐸 is the point of intersection of 𝐴𝐶 and 𝐵𝐷, 𝐴𝐸=5cm, 𝐸𝐶=8.9cm, 𝐸𝐷=7.7cm, and 𝑚𝐴𝐸𝐵=80. Give the answer to the nearest square centimeter.

Q7:

𝐴𝐵𝐶𝐷 is a parallelogram where 𝑀 is the point of intersection to the diagonals, 𝐴𝐶=21.1cm, 𝑚𝐴𝑀𝐷=8054 and 𝑚𝐶𝐴𝐵=5354. Find the area of the parallelogram giving the answer to two decimal places.

Q8:

In a parallelogram 𝐴𝐵𝐶𝐷, 𝐵𝐶=8inches and 𝐴𝐵=5inches, where 𝑚𝐴𝐵𝐶=134. Work out the length of 𝐴𝐶. Give your answer to 2 decimal places.

Q9:

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

Q10:

In a triangle 𝐴𝐵𝐶, 𝐴𝐵=3, 𝐴𝐶=8, and 𝑚𝐵𝐴𝐶=52.

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

Calculate the area of the triangle 𝐴𝐵𝐶 to 2 decimal places.

This lesson includes 120 additional questions and 1030 additional question variations for subscribers.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.