By definition,
[tex]\sin (angle)=\frac{\text{ opposite side}}{\text{ hypotenuse}}[/tex]
From the picture,
[tex]\begin{gathered} \sin (15^o)=\frac{BC}{60} \\ \sin (15^o)\cdot60=BC \\ 15.5\text{ ft = BC} \end{gathered}[/tex]
By definition,
[tex]\cos (angle)=\frac{\text{ adjacent side}}{\text{ hypotenuse}}[/tex]
From the picture,
[tex]\begin{gathered} \cos (15^o)=\frac{AC}{60} \\ \cos (15^o)\cdot60=AC \\ 58\text{ ft = AC} \end{gathered}[/tex]
AC is the base of the triangle and BC its height. Using the calculated values, the area of the triangle is:
[tex]\begin{gathered} A=\text{base}\cdot\text{height}\cdot\frac{1}{2} \\ A=\text{58}\cdot\text{15.5}\cdot\frac{1}{2} \\ A=449.5^{}\text{ ft}^2 \end{gathered}[/tex]
