Question

steps to construct a right angle triangle having hypotenuse of length 5.4 cm and one of the acute angle of measure 30 degree

Answer 1

Hope its clear this question hypotenuse is 5.4 cm A° = acute angle is 30°

Answer 2

$\bold{\large{\underline{\underline{Answer}}}}$

Steps of construction :

First of all make a rough diagram as a reference and mark hypotenuse as 5.4 and one angle measure 30°.

$\implies \bold{ AC \: = \: 5.4 \: cm }$

$\implies \bold{ \triangle{AOC} \: is \: right \: angle \: at \: 90^{\circ}}$

$\implies \bold{ acute \: \angle OCA \: = \: 30^{\circ} }$

Now ,

1 ) Draw a line with the help of ruler /scale of 5.4 cm.

2) Place the point of compass at C and make a arc or semi-circle.

3) Place the compass at point Q and mark an arc P` (by measuring it protector it's equal to 60°)

*Note compass distance always remain same

4) Now take compass on point Q and make a arc then from P` measure it with protractor it's become 30°.

The second acute angle

Angle sum property of triangle

$\bold{\angle{CAO} + \angle{AOC}+ \angle{ACO}\: = \: 180^{\circ}}$

$\bold{\angle{CAO} + 90^{\circ}+ 30^{\circ}\: = \: 180^{\circ}}$

$\bold{\angle{CAO} \: = \: 60^{\circ}}$

5) From the point C make a straight line passing through point Q`.

6) Now place the compass at point A and make a arc from point X from same distance of compass mark an point Y` from X angle make a straight line passing through it from point A.

7) Measure the sides if required and verify it by using Pythagoras Equation.

$\bold{\large{Thanks}}$