Question

A ladder, 26 m long, reaches the top of a house which is 10 m above
the ground, on one side of the street. Keeping its feet at the same
point, the ladder is turned to the other side of the street to reach the
top of another house. Find the height of the top of the other house,
if the street is 34 m wide.

Answer 24m​

Answer 1

Answer:

From figure △DAC  and  △EBC are right angled triangle.

So, by pythagorous theorem, we get

AC=24m  And,  CB=7m

Width of the street  =AC+CB

⟹24+7=31m

Note: The answer is wrong but from this method you will get your answer.

Hope it helps you

Answer 2

Given :

• A ladder is 26 m long.
• The ladder reaches the top of a house which is 10 m above the ground.
• The street is 34 m wide

Answer :

Let,

• AC = 26 m
• CE = 26 m
• ED = 10 m
• BD = 34 m
• BC = x m
• CD = 34 - x m
• AB = ?

$\displaystyle\underline{\bigstar\:\textsf{According to the given Question :}}$

In ∆DCE, By Phythagoras theorem :

➻ (EC)² = (ED)² + (CD)²

➻ (26)² = (10)² + (34 - x)²

➻ 676 = 100 + (34 - x)²

➻ (34 - x)² = 676 - 100

➻ (34 - x)² = 576

Taking square root to the both sides we get :

➻ 34 - x = √576

➻ 34 - x = 24

➻ x = 34 - 24

➻ x = 10 m

Now, In ∆ABC,By Phythagoras theorem :

➻ (AC)² = (AB)² + (BC)²

➻ (26)² = (AB)² + (x)²

➻ (26)² = AB² + (10)²

➻ 676 = AB² + 100

➻ AB² = 676 - 100

➻ AB² = 576

➻ AB = √576

➻ AB = 24 m

Therefore,the Height of the top of the tower is 24 m.