Question

How far up a wall will an 11 meter ladder reach, if the foot of the ladder must be 4 meters from the base of the wall? Round to the nearest hundredth.

Answer 1

Answer with explanation:

Length of ladder= 11 meter

Distance from foot of ladder to base of wall = 4 meter

Let height of Wall upto which Ladder reach = h meter

By using Pythagorean theorem

⇒(Length of ladder)²=(Height of Wall upto which Ladder reach)² + ( Distance from foot of ladder to base of wall)²

⇒(11)²=(Height of Wall upto which Ladder reach)²+4²

Subtracting 16 from both sides

⇒121 -16 = (Height of Wall upto which Ladder reach)²

⇒105 = (Height of Wall upto which Ladder reach)²

⇒ Height of Wall upto which Ladder reach

                           $=\sqrt{105}\\\\=10.2469\\\\=10.25 \text{meter}$                            

Answer 2

Use pythagorean theorem. 11m is the hypotenuse, while 4m is one of the legs. the wall should create a right angle with the ground which will allow for the pythagorean theorem. The height of where the ladder reaches will be named x.
x=√11^2-4^2=10.25m.