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](https://tex.z-dn.net/?f=%5Cimplies%5Cfrac%7BFA%7D%7BCA%7D%3D%5Cfrac%7BEF%7D%7BCB%7D%5C%5C%5C%5C%5Cimplies%20%5Cfrac%7B8%7D%7B40%7D%3D%5Cfrac%7B5%7D%7BCB%7D%5C%5C%5C%5C%5Cimplies%20CB%3D%5Cfrac%7B40%5Ctimes%205%7D%7B8%7D%5C%5C%5C%5C%5Cimplies%20CB%3D25)
Hence, The height of the tree = 25 feet