Respuesta :
Answer:
The distance from the ground to the top of the ladder = 18.7 feet
Step-by-step explanation:
The distance from the ground to the top of the ladder is 9 feet more than the distance from the building to the base of the ladder.
distance from the building to the base of the ladder.= X
The distance from the ground to the top of the ladder = 9+x
Solving the triangle using Pythagorean theorem
X² +(x+9)²= 21²
X² + x² + 18x +81= 441
2x² +18x -360 = 0
X² +9x -180 = 0
X= (-9-28.3)/2 or (-9+28.3)/2
Definitely x is going to be a positive number
So
X= (-9+28.3)/2
X=9.65 feet
The distance from the ground to the top of the ladder = 9+x
The distance from the ground to the top of the ladder = 9+9.65
The distance from the ground to the top of the ladder = 18.65
The distance from the ground to the top of the ladder = 18.7 feet
Building is 9.65 foot far from ladder.
Length of ladder = 21 foot. This diagonal ladder is Hypotenuse to the right angled triangle formed between building & ladder.
Let the distance from building to base of ladder = x. This is the base of right angled triangle.
So, distance from ground to top of ladder = x + 9. This is the height of right angled triangle.
As per Pythagorus Theorem,
[tex]Hypotenuse^2 = Base^2 + Height^2[/tex]
[tex]21^2 = x^2 + (x+9)^2[/tex]
441 = [tex]x^2 + x^2 + 81 + 18x[/tex]
360 = [tex]2x^2 + 18x[/tex]
[tex]2x^2 + 18x[/tex] - 360 = 0
x = -b + [tex]\sqrt{b^2 - 4ac[/tex] / 2a
x = 9.65 { Building distance to ladder base }
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