a tower cast a shadow of 16m at the same time that a 2.5m post cast a shadow of 4m. how high is the tower?

Question

explain

Answer 1

This is a proportion problem: 2.5 is to 4 as H is to 16. You can write these as fractions, then solve for the missing numerator. Since the denominator of the second fraction is four times that of the first, the numerator of the second fraction, H, must be four times that of the first, 2.5. So 4x2.5=10. The tower is 10 meters high.

Answer 2

you just need to work with Pythagoras...
(basically out of Pythagoras you only need to use the formula: tan x = opposite/adjacent)

in the post:

it is 2.5m tall, casts a shadow of 4m and (assumably) the post is at an angle of 90 degrees. But you need to know the angle that the Shadow makes on the ground (i really wish i could do this in a diagram....)

so: tan x = 2.5/4
x = tan-1(2.5/4)
x = 32 degrees (approximately)

now that you have this angle you can sub it into the other diagram as the angle that the shadow hits the ground.
you know need the height:

tan 32 = x/16
16(tan 32) = x
x = 10m (approximately)

so, the tower is 10m high...
of course, that's the way you're supposed to do it, you could always use ratios as it would work out really nicely:

tower - 16m shadow
post - 4m shadow

therefore: tower 4x larger than post
therefore: tower height = 2.5m x 4 = 10m

Answer 3

10 M

The tower casts a shadow that is 4 times longer than the shadow cast by the post. It would reason that the heigth of the tower is four times as high.

Answer 4

length of shadow of post / height of post = length of shadow of tower / height of tower

4/2.5=16/x
4x=2.5(16)
x=2.5(16)/4= 10 m

This question involves using a common ratio to find x.

Answer 5

10m

The towers shadow is 4 times larger, so it is 4 times taller.

2.5m x 4 = 10m

Answer 6

assuming equivalent placement of the light source... u can use basic proportionality theorem... if 'x' is the ht. of the tower... then... 2.5/x=4/16 => x = 10m... therefore ht. of the tower is 10m... chk out basic proportionality thm on wikipedia