Question

The length of the shadow of a tree is 10m less when the angle of elevation of the sun is

60 degree
. then when it is 45 degree
. Find out the height of the tree.​

Answer 1

Answer:

Step-by-step explanation:

Let H be the height of tree and x be the length of shadow

Consider ΔABD,

AB = H, BD = x @angle of elevation of 45°.

Tan45° = H/x

=> 1 = H/x

=> H = x    ---------------------- (1)

Given, when angle of elevation is 60°, the length of shadow is less by 10 m. Let C be be point at which angle of elevation is 60°

=> BC = x - 10

=> CD = 10 m.

Consider ΔABC

Tan60° = H/x - 10

=> √3 = H/x-10

=> H = √3(x-10) ------ (2)

But from (1) H = x, so substitute the value in (2)

=> x = √3x - 10√3

=> √3x - x = 10√3

=> x(√3 - 1) = 10√3

=> x = 10√3/(√3 - 1)

//multiply numerator and denominator by √3 + 1

=> x = 10√3/(√3 - 1)  * [√3 + 1 /√3 + 1]

        = 10√3(√3 + 1) / (√3 + 1)(√3 - 1)

        = 10√3(√3 + 1) / 3 - 1

         = 10√3(√3 + 1)/2

          = 5√3(√3 + 1)

          = 5*3 + 5√3

           = 15 + 5 * 1.732  (∵√3 = 1.732 approx.)

          = 15 + 8.66

          = 23.66 m. Approx.

Thus the height of tree is 23.66 m.