Question

Use FGH to match the measure below with its approximate value

Answer 1

Given data:

The first given side is FG=21.

The second given side is GH=12.

The expression for the Pythagoras theorem is,

`(FG)^2+(GH)^2=(FH)^2`

Substitute the given values in the above expression.

`\begin{gathered} (21)^2+(12)^2=(FH)^2 \\ 585=(FH)^2 \\ FH=24.18 \end{gathered}`

The expression for the angle F is,

`\begin{gathered} \tan (m\angle F)=(GH)/(GF) \\ =(12)/(21) \\ m\angle F=29.74^(\circ) \end{gathered}`

The angle H is,

`\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}`

Thus, the FH length is 24.18, m∠F=29.74 degrees, and m∠H is 60.26 degrees.