Answer
The measurement of side ‘a’ is \[\text{74 yd}\], measurement of side ‘c’ is\[\text{88 yd}\] and the measurement of angle B is \[33{}^\circ \].
Work Step by Step
Substitute the values in the above formula as mentioned below:
\[\begin{align}
& \text{tan 57}{}^\circ =\frac{a}{48} \\
& a=\text{tan 57}{}^\circ \times 48 \\
& =1.5412\times 48 \\
& \approx 74
\end{align}\]
It implies that: \[a\approx 74\text{ yd}\]
Now, in order to compute the value of c, use the trigonometric ratio of cos A as follows:
\[\cos \text{ }A=\frac{\text{Side adjacent to angle }A}{\text{Hypotenuse}}\]
\[\begin{align}
& \cos \text{57}{}^\circ =\frac{48}{c} \\
& c=\frac{48}{\cos \text{ 57}{}^\circ } \\
& =\frac{48}{0.5443} \\
& \approx 88
\end{align}\]
It implies that: \[c\approx 88\text{ yd}\]
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,
\[\begin{align}
& m\measuredangle A+m\measuredangle B+m\measuredangle C=180{}^\circ \\
& 57{}^\circ +m\measuredangle B+90{}^\circ =180{}^\circ \\
& m\measuredangle B=180{}^\circ -90{}^\circ -57{}^\circ \\
& =33{}^\circ
\end{align}\]
It implies that: \[\measuredangle B=33{}^\circ \]
Hence, the measurement of side denoted by ‘a’ is \[74\text{ yd}\], measurement of side denoted by ‘c’ is\[88\text{ yd}\] and the measurement of angle B is \[33{}^\circ \].
