plane trigonometry?

Question

1.When the suns angle of elevation is 30 degrees. The shadow of a post is 6 ft.longer than when the angle is 45 degrees . Find the height of the post.(show work)




2.Write the other functions of x if cos x= 3/5..(show work)

Answer 1

1.6ft/30=a/45
270=30*a
a=9ft
2.sinx=4/5
tanx=4/3=1/1/3
cosx2+sinx2=1
tanx=sinx/cosx

Answer 2

hctn(30) = hctn(45)+ 6
h(ctn 30 - ctn(45)) = 6
h = 6/(ctn 30 - ctn(45))
h = 4.3923 ft