Question

Find the length of the short leg on the following right triangle.

Answer 1

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

`\\or ( √(3) )/(2) = p / 10`

`or(10 √(3) )/(2) = p`

`or \: 5 √(3 ) = p`

Therefore,

`short \: leg = 5 √(3)`