142k views
0 votes
Find the length of the short leg of a 30 - 60 - 90 triangle If the long side is 4/3 units.

1 Answer

3 votes

Answer: CB=2/3

Explanation:

The triangle's angles are 30-60-90 degrees. So This is right triangle.

Let the triangle is ABC. B is right angle=90 degr . A=30 degrees, C=60 degrees

The long side of right triangle is hypotenuse AC=4/3 units.

In right triangle with 30 degr the side CB that is opposite to acute angle 30 degrees is twice shorter than hypotenuse AC

So CB=4/3/2=2/3

Finally using Pithagor theorem we find AB= sqrt( AC^2-CB^2)=

=sqrt(16/9-4/9)=sqrt(12/9)= 2*sqrt(3)/3

2*sqrt(3)/3>2/3 so AB>CB

So the shortest leg of ABC is CB=2/3

User Yang Yushi
by
5.3k points