Answer:
[tex]\alpha=57.72^o[/tex]
Step-by-step explanation:
Surface Area of a Cone
The surface area of a cone is given by
[tex]S=\pi r.h_s[/tex]
Where r is the radius and hs is the slant height measured from the top to any point at the circumference of the base. The cone shown in the figure has a radius r=3.4 and a surface area of 68.
Solving for hs
[tex]\displaystyle h_s=\frac{S}{\pi . r}[/tex]
[tex]\displaystyle h_s=\frac{68}{\pi \cdot 3.4}[/tex]
[tex]h_s=6.37[/tex]
But hs is equal to AS. The triangle SAO has an angle of 90° at the point O. The required angle m∠SAB can be found by applying the cosine ratio:
[tex]\displaystyle cos\alpha=\frac{AO}{AS}=\frac{3.4}{6.37}=0.53[/tex]
Thus
[tex]\boxed{\alpha=57.72^o}[/tex]
