# Lesson Worksheet: Law of Sines Mathematics

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:

For the given figure, and . Use the Law of Sines to work out . Give your answer to two decimal places. Q7:

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

Q8:

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

• A,
• B,
• C,
• D,

Q9:

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

• A
• B
• C
• D
• E

Q10:

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

Q11:

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

Q12:

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

• A
• B
• C
• D

Q13:

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

Q14:

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.

Q15:

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

Q16:

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. Q17:

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

Q18:

In triangle , , , and . Find the length of to the nearest tenth.

Q19:

is a triangle, where and the ratio between is . Find and , giving the answer to the nearest centimeter.

• A,
• B,
• C,
• D,

Q20:

is a triangle where , and . What type(s) could be?

• AObtuse
• BAcute
• CAcute or obtuse

Q21:

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

Q22:

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

Q23:

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

• A and
• B and
• C and
• D and

Q24:

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

Q25:

is a triangle where , and . Point lies on where . Find to the nearest degree and lengths , and giving the answers to two decimal places.

• A, , ,
• B, , ,
• C, , ,
• D, , ,