How high is a tree that casts a 21-ft shadow at the same time a 5-ft post a shadow which is 6ft long?The tree’s height is ___. (ft, ft^2, ft^3)(Round to the nearest tenth, I’d n…

Question

asked Apr 7, 2023 212k views

1 Answer

Martin Davies · Answer 1 · 2023-04-12T23:57:27+0000

Consider the following diagram,

Here, ED and BC are the heights of the tree and post respectively, while AD and AB are the lengths of the shadow cast by them, respectively.

According to the given information,

$\begin{gathered} AB=6 \\ AD=21 \\ BC=5 \end{gathered}$

Consider the tangent function of the angle A,

$\tan A=(BC)/(AB)=(ED)/(AD)$

Substitute the values and simplify,

$\begin{gathered} (5)/(6)=(ED)/(21) \\ ED=(5)/(6)\cdot21 \\ ED=17.5 \end{gathered}$

Thus, the tree's height is 17.5 feet.