The height from the ground at which the ladder touched the building is 12feet.
<h3>What is a right-angled triangle?</h3>
A right-angled triangle is a type of triangle that has three sides and one of its three angles as 90°.
Analysis:
The ladder length, height of the ladder from the ground, and the distance of the foot of the ladder from the foot of the building form a right angle triangle.
let x, be the distance from the foot of the building to the foot of the ladder.
x+7 = height of ladder from building to foot of building.
length of ladder = 13 feet
using Pythagoras, we have
= +
169 = + + 7x + 7x + 49
169 = 2 + 14x + 49
2 + 14x = 169-49
2 + 14x = 120
divide through by 2
+ 7x - 60 = 0
+12x -5x - 60 = 0
(x+12) -5(x+12) = 0
(x+12)(x-5) = 0
x = -12 or 5
Since measurement cannot be negative, therefore x = 5
Height the ladder touches the building is x+7 = 5+7 = 12 feet
Learn more about right-angled triangle: brainly.com/question/64787
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