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Example Questions
Example Question #1 : Law Of Sines
Given sides ,
and angle
determine the corresponding value for
Undefined
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
.
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 #1 : 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 #1 : Law Of Sines
By what factor is larger than
in the triangle pictured above.
It isn't
The Law of Sines states
so for a and b, that sets up
Example Question #38 : Law Of Cosines And 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.
cross-multiply
evaluate the right side
divide by 7
take the inverse sine
Example Question #39 : Law Of Cosines And 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:
cross-multiply
evaluate the sines
divide by 0.9063
Example Question #40 : Law Of Cosines And 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 #1 : 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 #1 : 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 #1 : 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:
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