Question

a vertical stick 20m long casts a shadow 10m long on ground.At the same time a tower cast a shadow 50m long on the ground .the height of tree is ?

Answer 1

Answer:

The height of the tree = 60 meters

Step-by-step explanation:

For better explanation of the answer see the figure attached :

Since, ∠C = ∠F because both are angles of incidence.

Now, in ΔABC and ΔDEF,

∠C = ∠F (Angles of incidence)

∠B = ∠D = 90°

So, By AA postulate of similarity of triangles,  ΔABC ~ ΔDEF

Now, Sides of similar triangles are proportional to each other.

$\implies \frac{AB}{DE}=\frac{BC}{EF}\\\\\implies \frac{x}{40}=\frac{12}{8}\\\\\implies x=\frac{12\times 40}{8}\\\\\bf\implies x = 60\textbf{ meters}$

Hence, The height of the tree = 60 meters

Answer 2

"“If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar”, this criterion in referred as (Angle–Angle–Angle) criterion of similarity of two triangles.

∠XYZ + ∠YZX + ∠ZXY = 180° = ∠ACB + ∠CBA + ∠BAC    

∠XYZ + ∠YZX + ∠ZXY = ∠ACB + ∠CBA + ∠BAC    

[(∠XYZ= ∠ACB  (Angle of shadow)@∠YZX= ∠CBA= 90 degree)]

∠ZXY = ∠BAC    

Therefore, using AAA similarity theorem $\Delta XYZ \sim \Delta ABC$.

$\frac{XZ}{AB} =\frac{ ZY}{BC} = \frac{XY}{AC}$

$\frac{XZ}{AB} =\frac{ ZY}{BC}$

$\frac{20}{AB} =\frac{10}{50}$

$\frac{(20\times50)}{10} = AB$

AB = 100 m.          

Therefore, the height of the tower is 100 m."