Question

how tall is a tree if it costs a shadow 59 degrees 24 minutes 41 inches on the ground 40 meter?

Answer 1

You need to rephrase the question, in better English. Are you sure the "41 inches" is not "41 arc seconds"? Is that angle the sun elevation angle? What does "on the ground 40 meter" mean? Is that the length of the shadow?

Answer 2

yes it is the lenght of the shadow.that is the problem that my professor gave me.

Answer 3

Theta = 59 deg 24' 41" = 59.4114 deg
is the solar elevation angle. (That is the angle that the sun is above the horizon)

Shadow length = 40 m = L cot (theta)
L = (Shadow length)*tan theta
= 40 tan 59.4114 = 67.67 m

Answer 4

A tree growing on a hillside casts a 121-foot shadow straight down
the hill. Find the height of the tree (in feet) if the slope of the hill is 8
and the angle of elevation of the sun from the horizontal is 50.