Question
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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.

Ask by Reese Mcfarlane. in the United States
Dec 10,2024

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Answer

The length of the side opposite the 40-degree angle is approximately 8.2.

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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!

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