Question

The tree casts a shadow 48ft long. At the same time of day an alien who is 7ft tall
casts a shadow 12ft long. What is the height of the tree? Explain or show all work.

Answer 1

Answer:

28 ft

Step-by-step explanation:

Since the shadows were cast at the same time of the day, both triangular images formed would be similar to each other.

Therefore, the ratio of their corresponding sides would be equal.

That is, the height of the tree / the height of the alien = the shadow of the tree / the shadow of the alien

Height of the tree = x ft

Height of the alien = 7 ft

Shadow of the tree = 48 ft

Shadow of the alien = 12 ft

Plug in the values into the proportional equation stated earlier.

Thus, the ratio of their corresponding sides would be:

$\frac{x}{7} = \frac{48}{12}$

Cross multiply

$x*12 = 48*7$

$12x = 336$

Divide both sides by 12

$x = \frac{336}{12}$

$x = 28$

The height of the tree = 28 ft