Question
4 A triangle has two angles that measures
110 degrees and 40 degrees. If the side
opposite the 110 degroes angle measures
12 , find the length of the side opposite
40 degree angle. round your answer
to nearest tenth.
110 degrees and 40 degrees. If the side
opposite the 110 degroes angle measures
12 , find the length of the side opposite
40 degree angle. round your answer
to nearest tenth.
Ask by Reese Mcfarlane. in the United States
Dec 10,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The length of the side opposite the 40-degree angle is approximately 8.2.
Solution

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Extra Insights
To find the length of the side opposite the 40-degree angle, we can use the Law of Sines. According to this rule, the ratio of the lengths of the sides of a triangle to the sines of their opposite angles is constant. Here, you can set it up like this:
Where
is the length of the side opposite the 40-degree angle,
is the length of the side opposite the 110-degree angle (which is 12), and
and
are the angle measures. After putting the numbers into the equation, you’ll find:
Solving for
gives you approximately
, when rounded to the nearest tenth.
Now you have your answer: the side opposite the 40-degree angle measures about 7.5 units. Happy calculating!