Find the unknown length in the figure given above↑↑↑↑
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A 13 m long laddar when set against the wall of a house reaches a height of 12 m . How far is the foot of the ladder from the wall.
Answers
Step-by-step explanation:
Solutions :-
1)
See the above attachments
From the figure,
In ∆ ADC , ∠ADC = 90°
It is a right angled triangle
AC = 50 m
AD = 14 m
We know that
By Pythagoras Theorem
AC² = AD²+DC²
=> 50² = 14² + DC²
=> 2500 = 196 + DC²
=> DC² = 2500-196
=> DC² = 2304
=> DC = ±√2304
=> DC = ± 48
therefore, DC = 48 m
Since, The length of the side can't be negative.
Now,
From ∆ ADB, ∠ ADB = 90°
It is a right angled triangle.
AB = 50 m
AD = 14 m
We know that
By Pythagoras Theorem
AB² = AD²+BD²
=> 50² = 14² + BD²
=> 2500 = 196 + BD²
=> BD² = 2500-196
=> BD² = 2304
=> BD = ±√2304
=> BD= ± 48
therefore, BD = 48 m
Since, The length of the side can't be negative
Now,
BC = BD+DC
=> x = 48+48 = 96 m
Therefore, x = 96 m
The value of x for the given problem is 96 m
2)
Length of the ladder = 13 m
Height of the wall = 12 m
On converting this situation as a diagram
we get a right angled triangle
Consider ∆ ABC
We have,
AB = 12 m
AB = 12 mAC = 13 m
The distance between the foot of the ladder from the wall is BC
Let BC = x m
We know that
By Pythagoras Theorem
AC ² = AB²+BC²
=> 13² = 12²+x²
=> 169 = 144+x²
=> 169-144 = x²
=> x² = 25
=> x = ±√25
=> x = ±5
Therefore, x = 5 m
Since, The distance can't be negative.
The distance between the foot of the ladder from the wall is 5 m
Used Theorem:-
Pythagoras Theorem
"In a right angled triangle,the square of the hypotenuse is equal to the sum of the squares of the other two sides".
Points to know :-
→ A triangle with one angle is right angle is called right angled triangle.
→ The opposite side to the right angle in a right angled triangle is called Hypotenuse.
→ The hypotenuse is the longest side in the right angled triangle.
