Question 600355
Since two sides measures 13 in, that means we are talking about an isosceles triangle.

the height of that triangle is the distance between the midpoint of the base and the meeting point of the other two sides. 
 That height is perpendicular to the base ( because it is an isosceles triangle)

By applying the Pythagorean Theorem, we get
 h^2 + (b\2)^2 =  s^2   ( where h represents the height , b the base and s one of the other sides.
   S0 we have  h^2 = s^2 - (b/2)^2
                   = 13^2 - (10/2)^2
                   = 169 - 25
                   = 144

 h^2 = 144 ,  so h = sqrt( 144) = 12

so the height is 12in