Question

At $4:00$ p.m. on a sunny day, a stick $2$ feet tall casts a shadow $5$ feet long. At the same time, a tree nearby casts a shadow $55$ feet long. What is the height in feet, of the tree ?

• A. $137.5$
• B. $27.5$
• C. $22$
• D. $10$

Answer 1

The correct option is C $22$

At the same time, the position of the sun will be fixed for both, hence the angle subtended by shadow on the tip of the tree will also be the same.

Let $x$ be the height of the tree in feet.

For stick,

$\tan \theta =\frac{2}{5}$

For tree,

$\begin{array}{cc}\tan \theta & =\frac{x}{55}\\ \frac{2}{5}& =\frac{x}{55}\\ x& =\frac{2\times 55}{5}\\ & =22\end{array}$