All Trigonometry Resources
Example Question #1 : Law Of Sines
Given sides , and angle determine the corresponding value for
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 #2 : Law Of Sines
Let , and , determine the length of side .
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
In the above triangle, and . If , what is to the nearest tenth? (note: triangle not to scale)
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 #4 : Law Of Sines
By what factor is larger than in the triangle pictured above.
The Law of Sines states
so for a and b, that sets up
Example Question #5 : Law Of Sines
Solve for :
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.
evaluate the right side
divide by 7
take the inverse sine
Example Question #6 : Law Of Sines
Evaluate using law of sines:
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:
evaluate the sines
divide by 0.9063
Example Question #7 : Law Of Sines
What is the measure of in below? Round to the nearest tenth of a degree.
The law of sines tells us that , where a, b, and c are the sides opposite of angles A, B, and C. In , these ratios can be used to find :
Example Question #8 : Law Of Sines
Find the length of the line segment in the triangle below.
Round to the nearest hundredth of a centimeter.
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 #9 : Law Of Sines
In the triangle below, , , and . What is the length of side to the nearest tenth?
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 .
What is the length of side a to the nearest tenth?
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: