Answer
The measurement of side ‘a’ is \[\text{54 cm}\], measurement of side ‘b’ is\[\text{67 cm}\] and the measurement of angle B is \[51{}^\circ \].
Work Step by Step
Substitute the values in the above function as follows:
\[\begin{align}
& \text{sin 39}{}^\circ =\frac{a}{86} \\
& a=\text{sin 39}{}^\circ \times 86 \\
& =0.629\times 86 \\
& \approx 54
\end{align}\]
It implies that: \[a\approx 54\text{ cm}\]
Now, in order to compute the value of c, use the trigonometric ratio of cos A as follows:
\[\text{cos }A=\frac{\text{Side adjacent to angle }A}{\text{Hypotenuse}}\]
Substitute the values in the above function as follows:
\[\begin{align}
& \text{cos 39}{}^\circ =\frac{b}{86} \\
& b=\text{cos 39}{}^\circ \times 86 \\
& =0.776\times 86 \\
& \approx 67
\end{align}\]
It implies that: \[b\approx 67\text{ cm}\]
Now, compute the third missing angle using angle sum property which specifies that sum of all angles of a triangle is equal to 180 degree.
Accordingly,
\[\begin{align}
& m\measuredangle A+m\measuredangle B+m\measuredangle C=180{}^\circ \\
& 39{}^\circ +m\measuredangle B+90{}^\circ =180{}^\circ \\
& m\measuredangle B=180{}^\circ -90{}^\circ -39{}^\circ \\
& =51{}^\circ
\end{align}\]
It implies that: \[\measuredangle B=51{}^\circ \]
Hence, the measurement of side denoted by ‘a’ is \[54\text{ cm}\], measurement of side denoted by ‘b’ is\[67\text{ cm}\] and the measurement of angle B is \[51{}^\circ \].
