Question

Find the value of sin c

Answer 1

Check the picture below.

`\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=√(a^2 + b^2) \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{7}\\ b=\stackrel{opposite}{√(95)}\\ \end{cases} \\\\\\ c=\sqrt{7^2~~ + ~~(√(95))^2}\implies c=√(49+95)\implies c=√(144)\implies c=12 \\\\[-0.35em] ~\dotfill\\\\ sin(C )=\cfrac{\stackrel{opposite}{√(95)}}{\underset{hypotenuse}{12}}\implies sin(C)\approx \text{\LARGE 0.81}`