Respuesta :
Answer:
5 meters.
Step-by-step explanation:
Given:
Mr. Dyer is leaning a ladder against the side of his house to repair the roof.
The top of the ladder reaches the roof, which is 3 meters high.
The base of the ladder is 4 meters away from the house, where Mr. Dyer's son is holding it steady.
Question asked:
How long is the ladder?
Solution:
Here we found that a right angle triangle is formed in which base and height is given and we have to find the longest side of the triangle.
Base = 4 meters
Height = 3 meters
Length of the ladder = ?
By Pythagoras theorem:
Square of longest side = Square of base + Square of height
[tex](Longest\ side)^{2} = 4^{2} +3^{2}[/tex]
[tex](Longest\ side)^{2} = 16+9[/tex]
[tex](Longest\ side)^{2} = 25[/tex]
Taking root both side :-
[tex]\sqrt[2]{(Longest\ side)^{2} } =\sqrt[2]{25}[/tex]
[tex]Longest\ side = \sqrt[2]{5\times5} \\ Longest\ side = 5[/tex]
Thus, length of ladder is 5 meters.
Answer:
The height of the ladder is 5 m.
Step by Step Explanation:
We have drawn diagram for your reference.
Given:
Distance of roof from base of the house = 3 m.
According to diagram;
AB = 3 m
Distance of the base of the ladder from the house = 4 m
According to diagram;
BC = 8 ft
We need to find the height of the ladder AC.
Solution:
Let us consider the scenario to be a right angled triangle with right angle at B.
So we will use Pythagoras theorem.
"In a right angle triangle square of sum of 2 sides is equal to square of the third side."
framing in equation form we get;
[tex]AC^2=AB^2+BC^2[/tex]
Substituting the given values we get;
[tex]AC^2=3^2+4^2\\\\AC^2=9+16\\\\AC^2=25[/tex]
Taking Square root on both side we get;
[tex]\sqrt{AC^2}=\sqrt{25}\\\\AC=5\ m[/tex]
Hence The height of the ladder is 5 m.
