Question

Need help ASAP. The diagram shows 5ft student standing near a tree. The shadow of the student and the shadow of the tree at endpoint A. What is the height of the tree. Show all your work, and make sure to include units in your final answer.

Answer 1

Answer:

The height of the tree = 25 feet

 Step-by-step explanation:  

From the given diagram : EF = 5 feet, FA = 8 feet, CA = 40 feet

∠AFE = 90° and ∠ACB = 90°

To find : CB, the height of the tree.  

Solution : In ΔAEF and ΔAB  C

∠AFE = ∠ACB = 90°  

∠A is common angle.  

So, By AA postulate of similarity of triangle, ΔAEF ~ ΔABC  

Now, sides of similar triangles are proportional to each other

$\implies\frac{FA}{CA}=\frac{EF}{CB}\\\\\implies \frac{8}{40}=\frac{5}{CB}\\\\\implies CB=\frac{40\times 5}{8}\\\\\implies CB=25$

Hence, The height of the tree = 25 feet