Explanation:
sadly we don't know anything about the size of the mirror on the ground, or if e.g. the 1.65 m from the mirror mean from the edge of the mirror or from the x at the center of the mirror.
so, we must assume the mirror as a dot without any significant lengths in the calculation.
we have 2 right-angled triangles.
1. the small one : from Yusuf's eyes to the ground at his feet to the x on the mirror on the ground.
2. the large one : from the top of the building to the bottom of the building on the ground to the x on the mirror on the ground.
the mirroring creates a dilation from the large triangle to the small triangle through the point x on the mirror.
in other words, all the angles stay the same, and there is one constant scale factor for all the lengths of one triangle to the other, making both triangles similar.
that means that the scale factor "f" of the ground distances from the small to the large triangle is
10.25 / 1.65 = 1025 / 165 = 6 35/165 = 6 7/33 =
= 6.212121212...
the scaling from Yusuf's height (well, his eye level) to the height of the school must follow the same ratio :
school height / Yusuf's eye level =
= h/1.55 = 10.25/1.65
h = 10.25 × 1.55 / 1.65 = 1025 × 155 / 16500 =
= 9.628787879... m ≈ 9.63 m
the school is approximately 9.63 m tall.
FYI : this is the same principle as with a camera. the lens (and the mirror inside if applicable) create a dilated "projection" onto a film or an array of digital light sensors, so that the captured image retains all the angles and all the length ratios of the original.
but to know from the picture e.g. how tall the original was, we need to know also the distance from which the picture was taken. otherwise this can't be answered.