Answer to Question #116865 in Trigonometry for Higgins

Question

In △ ABC, ∠C = 30o

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

Draw the triangle(s) and show 2 cases if there are two.

Answer 1

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

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

After putting the values of b,c and C=30$\degree$and 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).