Find the slant height of a cone with surface area 282.74 ft2 and diameter 10 ft.

The formula for the surface area of cone is:

Surface Area of Cone = π * r * l + π * r^2               , where l = slant height

Substituting the given values:

282.74 ft^2 = 3.14 * 5 ft * l + 3.14 * (5 ft)^2

l = 13 ft

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47

what chart am i supposed to follow?