Question 421478
draw a triangle and label it abc.


a is the projection of the sun from the top of the tower to the ground.


b is the base of the tower.


c is the top of the tower.


the height of the tower is bc
the length of the shadow is ab
ab is perpendicular to bc forming a 90 degree angle
the hypotenuse of the right triangle formed is ac


ab = 25 (length of shadow)
bc = 20 (height of tower)


the angle between sides ab and ac of the triangle is angle cab which we'll call angle x.


tan(x) = opp/adj = height of tower / length of shadow = bc / ab = 20/25 = .8


since the angle won't change, we can use tan(x) to find the height of the tower if the shadow was 75 meters.


we get tan(x) = opp/hyp = bc/ac 


tan(x) is .8
ac is 75


we want to find bc.


our equation becomes:


.8 = bc/75


multiply both sides of this equation by 75 to get:


.8*75 = bc which leads to bc = 60.


if the shadow were 75 meters, the height of the tower would be 60 meters.


a picture of the triangles formed is shown below:


<img src = "http://theo.x10hosting.com/problems/421478.jpg" alt = "***** picture not found *****" / >