Question

The height of a man and his shadow form a triangle similar to that formed by a nearby tree and its shadow. What is the height of the tree?

• A. 35 feet
• B. 20 feet
• C. 40 feet
• D. 30 feet

Answer 1

The correct option is C 40 feet

Here, $\Delta ABC\sim \Delta ADE$ (given)
Let the height of the tree is h feet,

∴ Their corresponding sides are proportional (by RHS similarity).
$\therefore \frac{AC}{AE}=\frac{BC}{DE}$
​​​​​​​$\frac{12}{96}=\frac{5}{h}$
$h=\frac{96\times 5}{12}=40$

∴ The height of the tree is 40 feet.