Please help? 10 Points for the first one who helps?

1) A monument consists of a flagpole 15 m tall standing on a mound in the shape of a cone with vertex angle 140 degree. How long a shadow does the pole cast on the cone where the angle of elevation fo the sun is 62 degree?





a) 10.52421m


b) 17.8218 m


c) 21.3793m


d) 12.3452 m








Thank you

Please help? 10 Points for the first one who helps?
Let:


AB be the flagpole,


BD be its shadow of length s,


DC be a horizontal line through D with C vertically below A,


k be the length of DC,


h be the length of BC.





Angle CBD = 70


Angle ACD = 62


AB = 15m





Triangle BCD:


h = k cot(70) ...(1)





Triangle ACD:


15 + h = k tan(62) ...(2)





Dividing (2) by (1):


1 + 15 / h = tan(62)tan(70)


15 / h = tan(62)tan(70) - 1


h = 15 / (tan(62)tan(70) - 1)





Triangle BCD:


s = h sec(70)


= 15 sec(70) / (tan(62)tan(70) - 1)


= 10.52421 m.





Answer (a).