SOLUTION: The height of a tower is 20 meters and the length of its shadow is 25 meters. What will be the height of the tower if its shadow is 75 meters at same time.
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Question 421478: The height of a tower is 20 meters and the length of its shadow is 25 meters. What will be the height of the tower if its shadow is 75 meters at same time.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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:
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