Question #116865
In △ ABC, ∠C = 30o

, c = 8.2cm, and b = 12.2cm.

Draw the triangle(s) and show 2 cases if there are two.
1
Expert's answer
2020-05-20T19:11:08-0400


The above figure shows the 2 triangles formed using the given data.

we have b=12.2 cm , c=8.2 cm and C=30°\degree b=12.2cm,c=8.2cm,and C=30°so by cosine formula, cos(30°)=a2+b2c22abb=12.2 cm, c=8.2 cm, and \ C=30 \degree so \ by \ cosine \ formula,\ cos(30\degree)=\frac {a^2 + b^2 -c^2} {2ab}

By solving the above equation, we get a22a.b.cos(30°)+b2c2=0a^2 -2a.b.cos(30\degree)+b^2-c^2=0 .

After putting the values of b,c and C=30°\degreeand solving the quadratic equation, we get the values of a = 16.05 cm and c=5.09 cm. Thus, there are 2 triangles shown above (2 cases).


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