A building is 110 feet tall When the angle of elevation of t

A building is 110 feet tall. When the angle of elevation of the sun is 25 degree, how long is it\'s shadow? Evaluate sin(arctan 1/3) sec (arccos 2/3) Verify the identity sin x(cot^2 x + 1) = csc x Verify the identity sec^2 x cot x - cot x = tan x

Solution

Lets shadow\'s length be h

tan 25=110/h

h=110/tan25=235.9ft

13. sin(tan^-1(1/3))

Let tan^-1(1/3)=t

therefore tan t=1/3

here opposite=1   and adjacent=3

hypotenuse=sqrt(1+9)=sqrt10

sin t= opposite/hypotenuse=1/sqrt10=sqrt10/10

Therefore sin(tan^-11/3)=sqrt10 / 10

b. sec(cos^-1(2/3))

Let cos^-1(2/3)=t

cos t=2/3

Therefore sect=3/2

Hence sec(cos^-1(2/3))=3/2