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.
From Pythagoras theorem and the ratio of legs
Hypotenuse will be at the ratio of
Multiplying the ratio of the sides of the triangle by ;
The length of the legs will be and and the hypotenuse
Procedure
I) A horizontal line is drawn.
On the left hand side of the line, the first vertex of the triangle is marked.
The compass is placed on a ruler and it is set to a length of .
The length is transported to the horizontal and with centre an arc that cut the horizontal line on the right of is marked as . 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 and two arcs that cut line AB at point and on opposite sides of are drawn.
Using as centre, an arc is drawn above line
Without adjusting the pair of compass and using as the centre, another arc is drawn so that the two arcs cut each other at point
is joined to and extended beyond
The pair of compass is adjusted to a radius of
With centre , an arc that cut produced is marked as
is joined to to complete the right angled triangle.
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