All Precalculus Resources
Example Questions
Example Question #11 : Use The Laws Of Cosines And Sines
Use the Law of Cosines to solve for the specified variable.
Solve for . Round to the nearest tenth.
None of these answers are correct.
Law of Cosines
Therefore...
After rounding...
Example Question #12 : Use The Laws Of Cosines And Sines
Use the Law of Sines to find in the following triangle.
(Not drawn to scale.)
We use the Law of Sines to solve this problem
we plug in
solving for we get:
Example Question #13 : Use The Laws Of Cosines And Sines
Use the Law of Sines to find .
(Not drawn to scale.)
We use the Law of Sines to solve this problem:
where
We plug in the values that we will need:
Notice that we did not use .
Solve for we get:
Example Question #14 : Use The Laws Of Cosines And Sines
Which of the following are the missing sides of the triangle?
None of the above
In order to solve this problem, we need to find . We do so by remembering the sum of the angles in a triangle is :
We can now use the Law of Sines to find the missing sides.
which is II.
which is III.
Our answers are then II and III
Example Question #15 : Use The Laws Of Cosines And Sines
Which of the following are the missing sides of the triangle?
None of the above
In order to solve this problem, we need to find
Since all the angles of a triangle add to , we can easily find it:
We can now use the Law of Sines to find the missing sides:
which is I.
which is III.
Our answers are then I and III.
Example Question #16 : Use The Laws Of Cosines And Sines
Solve the triangle using the Law of Sines:
None of the other answers
First we need to know what the Law of Sines is:
Looking at the triangle, we know c, C, and B. We can either solve for side b, using the law, or angle A using our knowledge that the interior angles of a triangle must add up to be 180.
Now all that's left is to find side a:
Example Question #17 : Use The Laws Of Cosines And Sines
Use the Law of Sines to solve for the specified variable.
Solve for . Round to the nearest tenth.
None of these answers are correct.
Law of Sines
Therefore...
After rounding...
Example Question #18 : Use The Laws Of Cosines And Sines
Solve for c using Law of Sines, given:
Round to the nearest tenth.
None of these answers are correct.
Law of Sines
Therefore...
After rounding...
Example Question #19 : Use The Laws Of Cosines And Sines
Given and , what is the measurement of to the nearest degree?
Using the information we have, we can solve for :
.
Plugging in what we know, we have:
.
Then, solve for :
.
Simplify, then solve for : which means .
Therefore, after rounding to the nearest degree, .
To solve for , subtract and from : .
Therefore, .
Example Question #20 : Use The Laws Of Cosines And Sines
Find the length of the missing side, .
First, use the Law of Sines to find the measurement of angle
Recall that all the angles in a triangle need to add up to degrees.
Now, use the Law of Sines again to find the length of .
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