Find the length of a ladder that is leaning against a wall.
A ladder leans against a wall at a point $8$ feet above the ground. The bottom of the ladder rests $2$ feet away from the wall. How long is the ladder?
$\endgroup$ 13 Answers
$\begingroup$Use Pythagorean Theorem: $a^2 + b^2=c^2$
Let $a=2$, $b=8$ and $c$ be the length of the ladder. Plug in your values and solve for C.
$\endgroup$ $\begingroup$From what I believe is the question this is just an easy application of the Pythagoras theorem
$a^2+b^2=c^2$
Where $c$ is the longest side and $b$ and $a$ are the other sides. So in your question, we know that $a=2$ and $b=8$ so we need to solve for $c$. We can plug the numbers in to get the answer
$2^2+8^2=c^2=68$ so $c=\sqrt{68}$ feet I believe
$\endgroup$ $\begingroup$$$\tan\theta = 8/2=4\implies \theta=\tan^{-1}4$$
Note that $$\sec\theta = h/2$$ $$2\sec\theta = h$$ $$h=2\sqrt{\tan^2\theta+1}=2\sqrt{\tan^2(\tan^{-1}4)+1}=2\sqrt{4^2+1}=2\sqrt{17}$$
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