A photograph taken at noon shows a tower and its shadow. In the photo the tower rises 12 cm, and the shadow attached to its base measures 3 cm. On the same day the actual shadow of the tower is known to be 27 m long.
a) Justify that the triangle formed by the tower and its shadow in the photograph is similar to the triangle formed by the actual tower and its shadow on the ground, clearly identifying corresponding sides.
b) Using the similarity, calculate the actual height of the tower.
c) The photograph is enlarged so that the height of the tower image on a poster becomes 30 cm. Compute
i) the new scale (number of metres of actual height represented by 1 cm on the poster), and
ii) the length on the poster that will represent the tower’s shadow.