Step 1

From the given data,

Consider the triangle ABD

Opposite side \(\displaystyle={g}\)

Hypotenuse \(\displaystyle{\left({c}\right)}={8.9}\)

\(\displaystyle\beta={63.5}^{{\circ}}\)

Step 2

We know that,

\(\displaystyle{{\sin{{63.5}}}^{{\circ}}=}{\frac{{{g}}}{{{8.9}}}}\)

\(\displaystyle{0.894934361}={\frac{{{g}}}{{{8.9}}}}\)

\(\displaystyle{g}={8.9}\times{0.894934361}\)

Therefore,

\(\displaystyle{g}={7.964915818}\) units.

Rounding off to the nearest tenth we have,

\(\displaystyle{g}={8.0}\) units is the required answer.

From the given data,

Consider the triangle ABD

Opposite side \(\displaystyle={g}\)

Hypotenuse \(\displaystyle{\left({c}\right)}={8.9}\)

\(\displaystyle\beta={63.5}^{{\circ}}\)

Step 2

We know that,

\(\displaystyle{{\sin{{63.5}}}^{{\circ}}=}{\frac{{{g}}}{{{8.9}}}}\)

\(\displaystyle{0.894934361}={\frac{{{g}}}{{{8.9}}}}\)

\(\displaystyle{g}={8.9}\times{0.894934361}\)

Therefore,

\(\displaystyle{g}={7.964915818}\) units.

Rounding off to the nearest tenth we have,

\(\displaystyle{g}={8.0}\) units is the required answer.