Question

The unknown triangle ABC has angle A= 44º and sides a = 15 and c= 20. How many solutions are there for triangle?

Answer 1

Step 1: '

Find the sides and the angles.

Apply sine rule to find angle C

Step 2

$\begin{gathered} \frac{a}{\sin A}\text{ = }\frac{c}{\sin C} \\ \frac{15}{\sin44}\text{ = }\frac{20}{\sin C} \\ \frac{15}{0.695}\text{ = }\frac{20}{\sin C} \\ \sin C\text{ = }\frac{20\times0.695}{15} \\ s\text{inC = 0.92666666} \\ C=sin^{-1}(0.9266666667) \\ C\text{ = 68} \end{gathered}$

Step 3

44 +

Step 4

Find side b

$\begin{gathered} \frac{a}{\sin A}\text{ = }\frac{b}{\sin B} \\ \frac{15}{\sin44}\text{ = }\frac{b}{\sin 68} \\ \frac{15}{0.695}\text{ = }\frac{b}{0.927} \\ b\text{ = }\frac{15\times0.927}{0.695} \\ b\text{ = 20} \end{gathered}$

Final answer

Since angle C = angle B, the length of the sides must also be equal.

Hence,

0 triangle