A man is standing on the top of a 40 foot tall building looking down at a bird that is standing on the roof of the building next door that is 25 feet tall. If the man is looking down to the bird at an angle of depression of 20°. what is the horizontal distance between the buildings feet? Round to the nearest hundredth.

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kiki4832

09.07.2021

Mathematics

The k-th root's inverse function is raising to the k-th power.

So, if we raise the k-th root of some number x to the k-th power, we have applied a function and its inverse to x, and we must get x itself as output:

$f(f^{-1}(x))=f^{-1}(f(x))=x\quad\text{for every invertible function f}$

So, in our case, we have

$(\sqrt[k]{x})^k = \left(x^{\frac{1}{k}}\right)^k=x^{k\cdot \frac{1}{k}}=x^1=x$

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