Question

The length of the Shadow of a tree when the angle of elevation of the sum is 60° is 6m less than length of the Shadow when the angle of elavation of the sum is 30°.Find the length of the tree​

Answer 1

Step-by-step explanation:

Let the height of the tree be h.

When the sun’s elevation is 60 deg, the shadow of the tree = h/tan 60 …(1)

When the sun’s elevation is 30 deg, the shadow of the tree = h/tan 30 …(2)

From (2) and (1) we have

h/tan 30 - h/tan 60 = 6, or

h(tan 60 - tan 30) = 6*tan 60 * tan 30, or

h = 6*tan 60 * tan 30/(tan 60 - tan 30) = 6(1.732050808 * 0.577350269)/(1.732050808 - 0.577350269) = 6/1.154700538 = 5.196152423 m.

The height of the tree is 5.196152423 m.