Question 1205051
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Answer: <font color=red size=4>Impossible</font>


Work Shown


Law of Sines
sin(𝛼)/a = sin(𝛽)/b 
sin(117)/11 = sin(𝛽)/24 
sin(𝛽) = 24*sin(117)/11 
sin(𝛽) = 1.94401 approximately


We stop here because the largest sin(𝛽) can get is 1. 
sin(𝛽) = 1.94401 has no real number solutions.
We cannot solve this triangle simply because a triangle cannot exist with these sides and angle. This is the SSA case.


Here's another approach.
𝛼 = 117° is the largest angle. It is obtuse. Any obtuse triangle will have exactly one angle between 90 and 180 degrees excluding both endpoints. 
The other two angles must be acute.


Since 𝛼 = 117° is the largest angle, the longest side must be side 'a'. 
Longest side is opposite the largest angle.


However, b = 24 is larger than a = 11. 
This contradiction is another way to see why this triangle is <font color=red>impossible</font>



More practice with solving a triangle.
<a href = "https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.1204286.html">https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.1204286.html</a>
and
<a href = "https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.1204365.html">https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.1204365.html</a>
and
<a href = "https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.1204423.html">https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.1204423.html</a>
and
<a href = "https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.1204634.html">https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.1204634.html</a>
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