Trigonometry : Law of Sines

Study concepts, example questions & explanations for Trigonometry

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Example Questions

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Example Question #1 : Law Of Sines

Figure1

Given sides  and angle  determine the corresponding value for 

 

Possible Answers:

Undefined

Correct answer:

Explanation:

The Law of Sines is used here since we have Side - Angle - Side. We setup our equation as follows:

Next, we substitute the known values:

Now we cross multiply:

Divide by 10 on both sides:

Finally taking the inverse sine to obtain the desired angle:

Example Question #1 : Law Of Sines

Let   and , determine the length of side .

Figure2

Possible Answers:

Correct answer:

Explanation:

We have two angles and one side, however we do not have . We can determine the angle using the property of angles in a triangle summing to :

Now we can simply utilize the Law of Sines:

Cross multiply and divide:

Reducing to obtain the final solution:

Example Question #3 : Law Of Sines

Triangle

In the above triangle,  and . If , what is  to the nearest tenth? (note: triangle not to scale)

Possible Answers:

Correct answer:

Explanation:

If we solve for , we can use the Law of Sines to find .

Since the sum of angles in a triangle equals ,

 

Now, using the Law of Sines:

 

Example Question #2 : Law Of Sines

Screen_shot_2015-03-07_at_5.09.32_pm

By what factor is  larger than  in the triangle pictured above.

Possible Answers:

It isn't

Correct answer:

Explanation:

The Law of Sines states

so for a and b, that sets up

Example Question #3 : Law Of Sines

Solve for :
Sines 1

Possible Answers:

Correct answer:

Explanation:

To solve, use the law of sines, where a is the side across from the angle A, and b is the side across from the angle B.

cross-multiply

evaluate the right side

divide by 7 

take the inverse sine 

 

Example Question #4 : Law Of Sines

Evaluate using law of sines:

Sines 2

Possible Answers:

Correct answer:

Explanation:

To solve, use law of sines, where side a is across from angle A, and side b is across from angle B.

In this case, we have a 90-degree angle across from x, but we don't currently know the angle across from the side length 7. We can figure out this angle by subtracting from :

Now we can set up and solve using law of sines:

cross-multiply

evaluate the sines

divide by 0.9063

Example Question #2 : Law Of Sines

What is the measure of  in  below? Round to the nearest tenth of a degree.

Triangle def

Possible Answers:

Correct answer:

Explanation:

The law of sines tells us that , where ab, and c are the sides opposite of angles AB, and C. In , these ratios can be used to find :

Example Question #5 : Law Of Sines

Find the length of the line segment  in the triangle below.

Round to the nearest hundredth of a centimeter.

Triangle

Possible Answers:

Correct answer:

Explanation:

The law of sines states that 

.

In this triangle, we are looking for the side length c, and we are given angle A, angle B, and side b. The sum of the interior angles of a triangle is ; using subtraction we find that angle C.

We can now form a proportion that includes only one unknown, c:

Solving for c, we find that 

.

Example Question #6 : Law Of Sines

In the triangle below, , and . What is the length of side  to the nearest tenth?

Triangle abc

Possible Answers:

Correct answer:

Explanation:

First, find . The sum of the interior angles of a triangle is , so , or .

Using this information, you can set up a proportion to find side b:

 

Example Question #10 : Law Of Sines

In the triangle below, , and .

Triangle abc

What is the length of side a to the nearest tenth?

Possible Answers:

Correct answer:

Explanation:

To use the law of sines, first you must find the measure of . Since the sum of the interior angles of a triangle is .

Law of sines:

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