Question

Two walls and a ceiling of a room meet
at right angles at a point P. A fly is in
the air 1 m from one wall, 8 m from
the other wall and 9 m from the point
P. How many meters is the fly from the
ceiling?

Answer 1

The position of the fly is shown as cross in the diagram below

The distance of the fly from the ceiling is given as $y$ 

We need to work out the distance $x$ to be able to work out the value of $y$

by the Pythagoras theorem

$x^{2} = 8^{2} + 1^{2}$
$x^{2} =65$
$x= \sqrt{65}$

by Pythagoras theorem

$y= \sqrt{9^{2}- ( \sqrt{65} )^{2} }$
$y = \sqrt{16} =4$

The distance of the fly from the point P is 4m