what s the value of x in its radical form in a 30-60-90 triangle or 45-45-90 triangle?

Question

The hypotenuse is 9 and one of the legs is 3 x in the value of the other leg. question doesn't say if its a 30-60-90 triangle or 45-45-90 triangle which confused me.

Answer 1

First draw the two different triangles, and label the sides accordingly as the problem states. 

Note that sin(30) = cos(60) = 1/2.  Knowing this, you can figure out the other side of the triangle and use Pythagorean theorem.

 

For the 30-60-90 triangle

 

(9/2)²+(3x)² = 9²

 

Solve for x.

 

For the 45-45-90 triangle (this is a right isosceles triangle)

 

(3x)²+(3x)² = 9²

 

Solve for x.