Question

Joe is fed up worrying about whether his neighbours can see into his living room from their house. He has decided to build a fence that is high enough to block the view from their top floor window. He needs to work out how high to build the fence. Find the minimum height of fence.

• A. 2.675 cm
• B. 2.744 m
• C. 2.675 m
• D. 2.75 cm

Answer 1

The correct option is C 2.675 m

Joe's measurements can be depicted in the figure shown above.

Let x be the unkown to be found out from the similar triangles but x is not the height of fence.

Let h be the height of the fence which will be equal to (x + 2) m.

Above shown two triangles are similar by AA similarity which says that if two corresponding angles are equal in two triangles then they are similar.
$\frac{1.8}{x}=\frac{8}{3}\frac{1.8\times 3}{8}=\frac{x}{1}x=0.675m$
Since h = x +2
h = 0.675 + 2
= 2.675 m
Hence, minimum height Joe has to build the fence is 2.675 m.