Question

151You mFind the value of x in the triangle shown bel=56°4.544What’s the value of x

Answer 1

Given:

Use the sin rule to find the missing angles,

$\begin{gathered} \frac{4}{\sin A}=\frac{4}{\sin B}=\frac{4.5}{\sin C} \\ \frac{4}{\sin56^{\circ}}=\frac{4}{\sin B}=\frac{4.5}{\sin x^{\circ}} \end{gathered}$

Now,

$\begin{gathered} \frac{4}{\sin56^{\circ}}=\frac{4.5}{\sin x^{\circ}} \\ \sin x^{\circ}=\frac{4.5\sin56^{\circ}}{4} \\ \Rightarrow x^{\circ}=\sin ^{-1}(\frac{4.5\sin56^{\circ}}{4}) \\ x^{\circ}=68.86^{\circ} \end{gathered}$