60+90+ angle U = 180 {sum of angle of triangle}
or, 150+ U= 180
or, angle U = 30°
From here we got that ,
angle U is smallest.
We know that, side opposite to the shortest angle is shortest side. So , short leg is side PM
In right angled triangle PMU,
hypotenuse(h) = 10
angle theta = 60°
perpendicular (PM)= ?
NOW,
sin theta = Perpendicular/ hypotenuse
or, sin 60° = P/10
[tex] \\or \frac{ \sqrt{3} }{2} = p \div 10[/tex]
[tex] or\frac{10 \sqrt{3} }{2} = p[/tex]
[tex]or \: 5 \sqrt{3 } = p[/tex]
Therefore,
[tex]short \: leg = 5 \sqrt{3} [/tex]
