Question

When the angle of elevation of the sun is 30° the shadow of a vertical tower is 20m longer than when the elevation of the sun is 60°.find the height of the tower

Answer 1

After making your sketch, .....
Let the shadow's length at 60° be x m, let the tower height be h
Given: the length of the shadow at 30° = x+20 m
so ... tan60 = h/x
h = xtan60
and tan 30 = h/(x+20)
h = tan30(x+20)

then xtan60 = tan30(x+20)
xtan60 = xtan30 + 20tan30
x(tan60 - tan30) = 20tan30
x = 20tan30/((tan60 - tan30) = ....

then you find h in h = xtan60

OR

Nice to have those 30° and 60° angles, since you have the 30-60-90 triangle
with corresponding sides in the ratio of 1:√3:2

By the 30-60-90 ratios:
√3 x / x = (x+2)/(√3x)
√3 = (x+20)/(√3x)
3x = x+20
x = 10
then h = √3x = √3(10) = appr 17.321.... m

You will get the same answer from my first solution.

Answer 2

Reiny's first solution can be made at least to look less complicated if you are comfortable using the cotangent function.
h cot30° - h cot60° = 20
h = 20/(cot30° - cot60°) = 20/(√3 - 1/√3)

Answer 3

I need the real solution to the question

Answer 4

i need the real solution t
o this answer pls