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} (a)/(\sin A)\text{ = }(c)/(\sin C) \\ (15)/(\sin44)\text{ = }(20)/(\sin C) \\ (15)/(0.695)\text{ = }(20)/(\sin C) \\ \sin C\text{ = }(20*0.695)/(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} (a)/(\sin A)\text{ = }(b)/(\sin B) \\ (15)/(\sin44)\text{ = }(b)/(\sin 68) \\ (15)/(0.695)\text{ = }(b)/(0.927) \\ b\text{ = }(15*0.927)/(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