Question

If you place a 16 ft ladder 6 feet from a wall, how high up the wall will it go?

Answer 1

Hint: In order to do this question, you have to consider a right angled triangle. The base of the triangle can be taken as 6 feet and the hypotenuse should be taken as 16 feet. Then we have to use the Pythagorean theorem that is $ {{x)}^{2}}+{{y}^{2}}={{z}^{2}}$. Here x is the height of the triangle, y is the base of the triangle and z is the hypotenuse of the triangle. To get the answer, we just have to find the y variable that gives us the height.

Complete step by step solution:
In the given question we are asked to find how high is the ladder when placed on a 16 ft ladder 6 feet from a wall.
To solve this, I have to consider a right angled triangle. The base of the triangle can be taken as 6 feet and the hypotenuse should be taken as 16 feet. Then we have to use the Pythagorean theorem that is $ {{x}^{2}}+{{y}^{2}}={{z}^{2}}$. Here x is the height of the triangle, y is the base of the triangle and z is the hypotenuse of the triangle. To get the answer, we just have to find the y variable that gives us the height.
$ \Rightarrow {{x)}^{2}}+{{y}^{2}}={{z}^{2}}$
Here x is the height, y = 6 ft, z = 16 ft. Substituting the values in the above equation, we get:
$ \Rightarrow {{x}^{2}}+{{6}^{2}}={{16}^{2}}$
$ \Rightarrow {{x}^{2}}=256-36=220$
$ \Rightarrow {x}=\sqrt{220}$
$ \Rightarrow {x}=14.83 ft$
So, therefore, by solving all the equations, we got the answer as 14.83 feet.

Therefore, the solution of the given question 14.83 ft or feet.

Note: In this question, you need to remember the Pythagorean theorem, otherwise, you cannot solve this problem. Also, if you want to have a clear understanding you could draw a triangle. And remember to place the units at the end of the answer.