Soh Cah Toa
Sine of the angle = opposite side over the hypotenuse
sin(42°) = 6.5/h
rearrange, solve for h
h = 6.5/sin(42°)
h = 9.7 cm
For the other triangle, the angle is unknown. I'd split it into two right triangles; down angle x since it is an isosceles it will be bisected into two equivalent triangles.
The hypotenuse we just found is now split in half. 9.7/2 = 4.9 base of the new smaller right triangle.
The new hypotenuse of the smaller triangle is 7.4 cm
Then you have..
sin(x/2) = 4.9/7.4
sin(x/2) = 0.67
use inverse sine function
arcSin(0.67) = x/2
41 = x/2
82° = x
There are many ways to solve this problem. This is just what I thought of first using trig.