Question

The length of the shadow of a tower standing on level ground is found to be 2x metres longer when the sun’s elevation is 30° than when it was 45°. The height of the tower in metres is
A. (√3+1)x
B. (√3-1)x
C. 2√3x
D.3√2x

Answer 1

tower height is

. C 2√3x

Answer 2

A. (√3+1)x

Step-by-step explanation:

Please refer to the attached picture for the diagram.

Let AB be the height of the tower h. Let distance BC be y metres.

In triangle ABC, tan 45 = AB/BC

 1 = h / y

 y = h -----------(1)

In triangle ABD, tan 30 = AB/BD

1/√3 = h/2x+y

 √3h = 2x+y

√3h = 2x + h

So x = 2x/ (√3-1)

     =  2x(√3+1) / 3-1

     = x(√3+1)

Option A is the answer.