Step-by-step explanation:
if I interpret this hand-written picture correctly, we have a major triangle with legs of 15 and 9, and a baseline that b is shot by the height into a segment of 6 and a segment of x.
I am not sure what the "*" symbols at the top mean. it cannot mean that both angles are the same. otherwise we would have an isoceles triangle (both legs are the same - this would be necessary, if both angles are the same; and vice versa).
anyway, the height of a triangle is always standing at 90° on the baseline.
this converts our main triangle into 2 right-angled triangles. and we can use Pythagoras to calculate the missing sides.
c² = a² + b²
c being the Hypotenuse (the baseline, the side opposite of the 90° angle), and a, b are the legs.
one triangle is 9, 6, height. 9 is the side opposite of the 90° angle and therefore the Hypotenuse :
9² = 6² + height²
81 = 36 + height²
height² = 45
height = sqrt(45) = 6.708203932...
the second triangle is 15, height, x. 15 is the side opposite of the 90° angle and therefore the Hypotenuse :
15² = height² + x²
225 = 45 + x²
x² = 180
x = sqrt(180) = sqrt(36×5) = 6×sqrt(5) = 13.41640786...
