the length of a hypotenuse of a 30 60 90 triangle is 4, find the longer leg

Question

don't know I just need help please I don't understand it at all

Answer 1

If you don't know trigonometry:

 

   In a 30-60-90 triangle, the length of the side opposite the 30° angle is half the length of the hypotenuse and the length of the side opposite the 60° angle is √3 times as long as the side opposite the 30° angle.  

 

So, since the hypotenuse has length 4, the side opposite the 30° angle has length 2 and the side opposite the 60° angle has length 2√3 (the length of the longer leg).

Answer 2

r= length hypotenuse;  

x=length adjacent;  y=length opposite

By definition:   cos(θ)=x/r   and  sin(θ)=y/r

so using algebra:    x=rcos(θ)   and   y=rsin(θ) 

If θ=30^o:  x=4cos(30^o)=4(√3/2)=2√3 

and y=4sin(30^o)=4(1/2)=2