Question

A ladder, 8m long, leans against a vertical wall with the foot of the ladder 1.4m away from the wall. How high up the wall does the top of the ladder reach?

Answer 1

The diagram can be thought of as a right triangle with a hypotenuse of 8m, and a base of 1.4m. We can solve for the vertical height by using Pythagorean theorem.

`\begin{gathered} a^2+b^2=c^2 \\ \text{where} \\ c\text{ is the hypotenuse or the longest side of the right triangle} \\ a\text{ and }b\text{ are the other two sides of the triangle} \\ \\ \text{Given} \\ \text{hypotenuse of 8m}=c \\ \text{base of 1.4m}=b \end{gathered}`

Substitute the following given to the Pythagorean theorem and we have

`\begin{gathered} a^2+b^2=c^2 \\ a^2+(1.4\text{ m})^2=(8\text{ m})^2 \\ a^2+1.96\text{ m}^2=64\text{ m}^2 \\ a^2=64\text{ m}^2-1.96\text{ m}^2 \\ a^2=62.04\text{ m}^2 \\ \sqrt[]{a^2}=\sqrt[]{62.04\text{ m}^2} \\ a=7.8765474670060866713113634659718\text{ m} \\ a\approx7.9\text{ m} \end{gathered}`

Therefore, it is 7.9 m high up the wall where the top of the ladder reach.