Lesson Worksheet: Law of Sines Mathematics

In this worksheet, we will practice using the law of sines to find the sides and angles of a triangle and solve real-life problems.

Q1:

A small triangular flower bed has measurements as shown in the diagram. Calculate its area in square feet. Give your answer to two decimal places.

Q2:

Which of the following is a formula that can be used to find the area of a triangle?

  • A12𝑎𝑏𝐶sin
  • B14𝑎𝑏𝐶cos
  • C13𝑎𝑏𝐶sin
  • D14𝑎𝑏𝐶sin
  • E12𝑎𝑏𝐶cos

Q3:

In the given figure, work out the area of the triangle to 2 decimal places.

Q4:

𝐴𝐵𝐶 is a triangle, where 𝐵𝐶=15cm, 𝐴𝐶=25cm, and 𝑚𝐶=41. Find the area of 𝐴𝐵𝐶, giving your answer to three decimal places.

Q5:

An isosceles triangle has two sides of length 48 cm and base angles of 73. Find the area of the triangle giving the answer to three decimal places.

Q6:

𝐴𝐵𝐶 is a triangle where 𝐴𝐵=18cm, 𝑚𝐵=60 and the area of the triangle is 743 cm2. Find length 𝐵𝐶 giving the answer to two decimal places.

Q7:

𝐴𝐵𝐶 is a triangle where 𝐴𝐵=5cm, 𝐴𝐶=11cm, and 𝑚𝐴=107. Find the area of the triangle giving the answer to two decimal places.

Q8:

For the given figure, 𝐴𝐵=3 and 𝐵𝐶=𝑎. Use the Law of Sines to work out 𝑎. Give your answer to two decimal places.

Q9:

𝐴𝐵𝐶 is a triangle, where 𝑚𝐴=461117, 𝑚𝐵=27446, and length 𝑎=21.4cm. Find the length of the shortest side of 𝐴𝐵𝐶 giving the answer to one decimal place.

Q10:

𝐴𝐵𝐶 is a right triangle at 𝐵. The point 𝐷 lies on 𝐵𝐶, where 𝐶𝐷=17cm, 𝑚𝐴𝐷𝐶=46, and 𝑚𝐶𝐴𝐷=24. Find the length of 𝐴𝐵, giving your answer to the nearest centimeter.

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