Question #266007

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.


1
Expert's answer
2021-11-15T16:36:36-0500

From Pythagoras theorem and the ratio of legs

Hypotenuse will be at the ratio of

32+42\sqrt{3^2+4^2} =5=5


Multiplying the ratio of the sides of the triangle by 22 ;

The length of the legs will be 6cm6cm and 8cm8cm and the hypotenuse 10cm10cm


Procedure


I) A horizontal line is drawn.

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


The compass is placed on a ruler and it is set to a length of 8cm8cm.

The length is transported to the horizontal and with centre A,A,\>an arc that cut the horizontal line on the right of AA is marked as BB . 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 BB and two arcs that cut line AB at point PP and QQ on opposite sides of BB are drawn.


Using PP as centre, an arc is drawn above line ABAB


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


BB is joined to RR and extended beyond RR


The pair of compass is adjusted to a radius of 6cm6cm


With centre BB , an arc that cut BRBR produced is marked as CC


CC is joined to AA to complete the right angled triangle.


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