Given:
The measure of angle ∠H = 27°.
The measure of length HI is 8.
The objective is to find the measure of GI.
Explanation:
Considering the angle ∠H°, the side GI is the opposite side and the side HI is the adjacent side.
So considering the trigonometric ratio of tanθ,
[tex]tanH=\frac{\text{opposite}}{\text{adjacent}}\text{ . . . . . }(1)[/tex]
On plugging the given values in equation (1),
[tex]\begin{gathered} \tan 27\degree=\frac{GI}{8} \\ GI=\tan 27\degree\times8 \\ GI=4.076203\ldots.. \\ GI\approx4.1 \end{gathered}[/tex]
Hence, the measure of length GI is 4.1.
