Question

At 5 feet tall, Emily casts a shadow that is 8 feet long. She is standing near a tree that casts a shadow that is 28 feet long. How tall is the tree?

Answer 1

Answer:

The tree is 17.5 ft tall

Step-by-step explanation:

We can use proportions to solve this.

Notice that Emily (5 feet tall) and her shadow (8 feet long) constitute the two legs of a right angle triangle (see attached image).

The nearby tree  (unknown height H), will also cast a shadow (28 ft long) with the same inclination as Emily does due to the unique position of the sun relative to them.

Then we can use the proportion associated with the sides of similar triangles:

$\frac{5\,ft}{8\,ft} =\frac{H}{28\,ft}$

Then, we can solve for H in the equation:

$\frac{5\,ft}{8\,ft} =\frac{H}{28\,ft} \\H=\frac{28*5}{8} \,ft\\H=17.5 \.ft$