Given data:
The first given side is FG=21.
The second given side is GH=12.
The expression for the Pythagoras theorem is,
[tex](FG)^2+(GH)^2=(FH)^2[/tex]
Substitute the given values in the above expression.
[tex]\begin{gathered} (21)^2+(12)^2=(FH)^2 \\ 585=(FH)^2 \\ FH=24.18 \end{gathered}[/tex]
The expression for the angle F is,
[tex]\begin{gathered} \tan (m\angle F)=\frac{GH}{GF} \\ =\frac{12}{21} \\ m\angle F=29.74^{\circ} \end{gathered}[/tex]
The angle H is,
[tex]\begin{gathered} m\angle H+m\angle G+m\angle F=180\circ \\ m\angle H+90^{\circ}+29.74^{\circ}=180^{\circ} \\ m\angle H=60.26^{\circ} \end{gathered}[/tex]
Thus, the FH length is 24.18, m∠F=29.74 degrees, and m∠H is 60.26 degrees.
