Question

The given diagram shows how it post was broken. What was the original height of the post, in inches?

Answer 1

Assuming that the post is right-angled to the ground, we can solve for the length of the broken slanted post using the Pythagorean Theorem. After getting the length of the slanted post, we'll add the result to the 24 inches to find the original height of the post.

So, the Pythagorean Theorem is:

`c=\sqrt[]{a^2+b^2}`

where c = hypotenuse = slanted post, "a" and "b" are the legs of the triangle. Let's plug in a = 18 inches and b = 24 inches and solve.

`c=\sqrt[]{18^2+24^2}`
`\begin{gathered} c=\sqrt[]{324+576} \\ c=\sqrt[]{900} \\ c=30inches \end{gathered}`

Therefore, the length of the broken slanted post is 30 inches.

Adding this length to the 24 inches length of the remaining post, we get:

`30\text{inches}+24inches=54inches`

Therefore, the original height of the post is 54 inches.