Question

When a tree 8m high casts a shadow 3m ​long, how long is a shadow cast by a person 2m ​tall?

Answer 1

x = 3/4 m

Explanation:

Construct two similar right triangles that share an angle of elevation. The two vertical sides represent the heights of the person and the tree and are 2 m ad 8 m respectively. The two horizontal sides represent the shadow cast by the person and that cast by the tree, respectively. Because the triangles are similar, we can write the following equation of ratios:

8 m 3 m

--------- = --------

2 m x

... where x is the length of the shadow cast by the person.

Cross multiplying, we get:

8x = 6m, or x = 6/8 m, or x = 3/4 m

Answer 2

3/4 meters

Explanation:

We can use ratios to solve

8m 2 m

------- = -----------

3m x m

Using cross products

8*x = 3*2

Divide each side by 8

8x/8 = 6/8

3/4 meters