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Worksheet: The Law of Sines

Q1:

is a triangle, where , , and . Find the length of , giving your answer to one decimal place.

Q2:

Find all the angles and lengths of the given triangle, giving the lengths to three decimal places and angles to the nearest degree.

  • A , ,
  • B , ,
  • C , ,
  • D , ,

Q3:

Find all the angles and lengths of the given triangle, giving the lengths to three decimal places and angles to the nearest degree.

  • A , ,
  • B , ,
  • C , ,
  • D , ,

Q4:

Find all the angles and lengths of the given triangle, giving the lengths to three decimal places and angles to the nearest degree.

  • A , ,
  • B , ,
  • C , ,
  • D , ,

Q5:

is an isosceles triangle where and . Find the length of giving the answer to one decimal place.

Q6:

is an obtuse triangle at , where , , and . Find giving the answer to the nearest minute.

  • A
  • B
  • C
  • D
  • E

Q7:

is an obtuse triangle at , where , , and . Find giving the answer to the nearest minute.

  • A
  • B
  • C
  • D
  • E

Q8:

is a triangle, where , , and . Find the value of , giving the answer in terms of .

  • A
  • B
  • C
  • D
  • E

Q9:

is a triangle where and . Find giving the answer to the nearest whole number.

Q10:

A house is 66 meters tall. The angle of elevation from the base of the house to the top of a tower is , and the angle of elevation from the top of the house to the top of the tower is . Find the height of the tower giving the answer to the nearest meter.

  • A 81 m
  • B 233 m
  • C 181 m
  • D 147 m

Q11:

The figure shows three peaks in a mountain range , , forming a triangle. The distance between and is 24.7 km, the angle at is and the angle at is . Find the area of the triangle giving the answer to two decimal places.

Q12:

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