All High School Math Resources
Example Questions
Example Question #1 : Law Of Sines
In this figure, angle and side . If angle , what is the length of side ?
For this problem, use the law of sines:
.
In this case, we have values that we can plug in:
Cross multiply:
Multiply both sides by :
Example Question #1 : Law Of Sines
In this figure and . If , what is ?
For this problem, use the law of sines:
.
In this case, we have values that we can plug in:
Example Question #1 : Applying The Law Of Sines
In , , , and . To the nearest tenth, what is ?
Since we are given and want to find , we apply the Law of Sines, which states, in part,
and
Substitute in the above equation:
Cross-multiply and solve for :
Example Question #11 : Triangles
In , , , and . To the nearest tenth, what is ?
No triangle can exist with these characteristics.
Since we are given , , and , and want to find , we apply the Law of Sines, which states, in part,
.
Substitute and solve for :
Take the inverse sine of 0.6355:
There are two angles between and that have any given positive sine other than 1 - we get the other by subtracting the previous result from :
This, however, is impossible, since this would result in the sum of the triangle measures being greater than . This leaves as the only possible answer.
Example Question #2 : Law Of Sines
In this figure, angle . If side and , what is the value of angle ?
Undefined
For this problem, use the law of sines:
.
In this case, we have values that we can plug in:
Example Question #1 : Applying The Law Of Sines
In this figure, if angle , side , and side , what is the value of angle ?
(NOTE: Figure not necessarily drawn to scale.)
Undefined
First, observe that this figure is clearly not drawn to scale. Now, we can solve using the law of sines:
.
In this case, we have values that we can plug in: