# Worksheet: Law of Sines

In this worksheet, we will practice applying the law of sines to find lengths and angle measures in non-right triangles.

Q1:

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

Q2:

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

• A and
• B and
• C and
• D and

Q3:

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

Q4:

is a triangle where . Find the ratio .

• A
• B
• C
• D
• E

Q5:

is a triangle where and . Find the ratio of lengths .

• A
• B
• C
• D

Q6:

In triangle , , , and . Determine the length of to the nearest meter.

Q7:

For the given figure, and . Use the Law of Sines to work out . Give your answer to two decimal places. Q8:

is a triangle, where , , and . Find to the nearest tenth of a degree.

Q9:

is an obtuse-angled triangle at where , and . Find lengths and giving the answer to the nearest integer.

• A and
• B and
• C and
• D and

Q10:

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

• A
• B
• C
• D
• E

Q11:

The diameter of a circle is 82 cm. and are two chords on opposite sides of a circle with lengths 5.1 cm and 48.4 cm respectively. Find the length giving the answer to two decimal places.

Q12:

is a triangle where and the perimeter is 169 cm. Find the values of and giving the answer to the nearest centimeter.

• A and
• B and
• C and
• D and

Q13:

Which rule could be used to find the length of an unknown side of a triangle, given the measures of two angles and the length of one other side?

• Asine rule
• Bcosine rule
• Cdouble angle rule
• Dangles sum rule
• Etangent rule

Q14:

Two men are standing in front of a minaret at the points and respectively where the distance between them is 25.4 m. Find the height of the minaret giving the answer to one decimal place. Q15:

is a triangle where , and . Find giving the answer to the nearest second.

• A
• B
• C
• D

Q16:

In the figure . Q17:

The scale of a map is . The positions of three towns on a map form a triangle. Towns B and C are 17 cm apart, and the angles and are and respectively. Find the actual distance between towns A and B and between towns A and C, giving the answer to the nearest kilometer. • AThe actual distance between cities A and B is 12 km, and the actual distance between cities A and C is 21 km.
• BThe actual distance between cities A and B is 36 km, and the actual distance between cities A and C is 21 km.
• CThe actual distance between cities A and B is 12 km, and the actual distance between cities A and C is 7 km.
• DThe actual distance between cities A and B is 9 km, and the actual distance between cities A and C is 16 km.

Q18:

is an equilateral triangle of side length 12 cm that is inscribed in a circle. Find the radius of the circle, giving the answer to two decimal places.

Q19:

is a right triangle at . The point lies on , where , , and . Find the length of , giving your answer to the nearest centimeter.

Q20:

is a triangle with a perimeter of 49 cm where the ratio between , and is . Find the length of the smallest side giving the answer to two decimal places.

Q21:

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

Q22:

In the given figure, is a rectangle and is a point on the straight line . , , and . Find the length of giving the answer to the nearest meter. Q23:

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

Q24:

, and represent three coffee shops along a river bank. is on one side and and are on the other. is located where and . Find the distance between and and the width of the river giving the answers to two decimal places. • A. Width of river .
• B. Width of river .
• C. Width of river .
• D. Width of river .

Q25:

is a triangle where , and . Find all possible values of giving the answer to the nearest second.

• A or
• B
• C or
• D
• E or