Answer
The measurement of side ‘a’ is \[18\text{ yd}\], measurement of side ‘c’ is\[29\text{ yd}\] and the measurement of angle B is \[50{}^\circ \].
Work Step by Step
Substitute the values in the above formula as mentioned below:
\[\begin{align}
& \text{tan 40}{}^\circ =\frac{a}{22} \\
& a=\text{tan 40}{}^\circ \times 22 \\
& =0.8395\times 22 \\
& =18.4707
\end{align}\]
It implies that: \[a\approx 18\text{ yd}\]
Now, in order to compute the value of c, use the trigonometric ratio of cos A as follows:
\[\cos A=\frac{\text{Side adjacent to angle }A}{\text{Hypotenuse}}\]
Substitute the values in the above formula as follows:
\[\begin{align}
& \cos \text{40}{}^\circ =\frac{22}{c} \\
& c=\frac{22}{\cos \text{40}{}^\circ } \\
& =\frac{22}{0.7658} \\
& =29
\end{align}\]
It implies that: \[c\approx 29\text{ yd}\]
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,
\[\begin{align}
& m\measuredangle A+m\measuredangle B+m\measuredangle C=180{}^\circ \\
& 40{}^\circ +m\measuredangle B+90{}^\circ =180{}^\circ \\
& m\measuredangle B=180{}^\circ -90{}^\circ -40{}^\circ \\
& =50{}^\circ
\end{align}\]
It implies that: \[\measuredangle B=50{}^\circ \]
Hence, the measurement of side denoted by ‘a’ is \[18\text{ yd}\], measurement of side denoted by ‘c’ is\[29\text{ yd}\] and the measurement of angle B is \[50{}^\circ \].
