Answer to Question #266007 in Geometry for S.S

Question

Describe the algorithm of constructing (using a compass and a ruler) a right-angled triangle knowing its hypotenuse and the ratio of its legs being equal to ¾.

Answer 1

From Pythagoras theorem and the ratio of legs

Hypotenuse will be at the ratio of

$\sqrt{3^2+4^2}$ $=5$

Multiplying the ratio of the sides of the triangle by $2$ ;

The length of the legs will be $6cm$ and $8cm$ and the hypotenuse $10cm$

Procedure

I) A horizontal line is drawn.

On the left hand side of the line, the first vertex $A$ of the triangle is marked.

The compass is placed on a ruler and it is set to a length of $8cm$.

The length is transported to the horizontal and with centre $A,\>$an arc that cut the horizontal line on the right of $A$ is marked as $B$ . This is the second vertex of the triangle.

The pair of compass is adjusted to a suitable radius.

The sharp point of the pair of compass is placed at point $B$ and two arcs that cut line AB at point $P$ and $Q$ on opposite sides of $B$ are drawn.

Using $P$ as centre, an arc is drawn above line $AB$

Without adjusting the pair of compass and using $Q$ as the centre, another arc is drawn so that the two arcs cut each other at point $R$

$B$ is joined to $R$ and extended beyond $R$

The pair of compass is adjusted to a radius of $6cm$

With centre $B$ , an arc that cut $BR$ produced is marked as $C$

$C$ is joined to $A$ to complete the right angled triangle.