Use Pythagorean Theorem. a^2 + b^2 = c^2 Substitute the numbers. 12^2 + b^2 = 20^2 144 + b^2 = 400 Subtract 144 from each side. b^2 = 256 Take square root. The answer is b = 16
The height of the building to which the ladder reaches is:
16 ft.
<h2>Step-by-step explanation:</h2>
We can model this problem with the help of a right angled triangle ΔABC such that the hypotenuse of the triangle is 20-ft and one of it's leg is: 12 ft.
Now we are asked to find the other leg of the triangle.
We will use the Pythagorean Theorem in order to find the other leg.
Pythagorean Theorem says that: If c is the hypotenuse of the right triangle and a and b are it's two legs then,
Hence, here we have:
So,
Since, b can't be negative as it denotes a side of a triangle.
Multiply first equation by 2: 10x + 2y = 18 Subtract the second equation from this so that the 2y terms cancel: 10x - 3x = 18 - 4 7x = 14 x = 2 Plug into first equation to find y: 5(2) + y = 9 10 + y = 9 y = -1 The answer is (2,-1)