how tall is this tree?

Question

at a particular time, a tree casts a shadow 28m long on the ground. at the same time, a nearby vertical pole that is 3m high casts a shadow 4 m long. how tall is the tree

Answer 1

Set this up as a ratio:
Pole height : Pole shadow = Tree height : Tree shadow
3 is to 4 as x is to 28

3/4 = x/28
x = 28 * 3/4
x = 21

So the tree is 21m tall.

Answer 2

Treat them as similar right triangles.

The tree and its shadow form two legs of one triangle (call it A).
The pole and its shadow form two legs of another triangle (call it B).

Now, A and B are similar because the tree and the pole are perpendicular to the ground (right angles) and the sun is in the same position (meaning that the angle that it casts the shadow are congruent for both tree and pole).

One property of similar triangles is that the sides of A are all in the same proportion of the sides of B. The shadow of the pole is 4 meters, while the shadow of the tree is 28 meters. Thus, A is 7 times the size of B.

Since you know the pole is 3 meters high, you multiply that by 7 to figure out that the tree is 21 meters high.

Answer 3

28 is 7 times 4, therefore the height of the tree is 7 x 3m = 21m. Similar triangles.

Answer 4

The answer is 21. How you get it is the following:

(Note: tree = t pole = p shadow t = st shadow p = sp)

St = 28m /Sp=4m =7m

P =3m T =p x 7m T = 3m x 7m =21m

Answer 5

Good ratio problem:

h/28 = 3/4

This is true because the lengths involved are for similar triangles. All angles are the same and so corrosponding lengths are scaled.

Now, solve for h.

Answer 6

h = height of tree
h/28 = 3/4
cross multiply:
4h = 84
h = 21
The tree is 21 meters high.

Answer 7

x/28 = 3/4
x = 3*28/4
x = 21