Question

Solve this asap please

Answer 1

a) See attached image

b) AA (or AAA) similarity; either one is correct

c) The statue is 22 meters tall

Explanation:

Let's assume the height of the statue is h (to be determined)

a) First let's create a diagram to model this scenario. See attached image
One of the properties of a mirror reflection is that the angle of incidence i.e. the angle at which light strikes the mirror = angle of reflection i.e. the angle at which the light reflects off the mirror

These angles are shown as α and β in the diagram

The two triangles we choose to solve this problem are
ΔABC and ΔCED

Given that ∠BCA is a complementary angle to angle of reflection and ∠ECD is complementary to the angle of incidence, it follows that

m∠BCA = m∠CED

m∠BAC of ΔABC = m∠ECD of ΔECD = 90°

Therefore the third angles of both triangles are also equal

b) By the AA (or AAA) or Angle-Angle Similarity theorem, the two triangles are similar

Therefore the ratio of the sides must be the same for corresponding sides

Therefore

`(AB)/(DE) = (AC)/(CD) \\\\Given AD = 12, CD = 3\\\\(AD)/(CD) = (12)/(3)= 4\\\\\therefore \\\\(AB)/(ED) = 4\\\\`

Since ED is the height of the girl = 5.5 meters and AB = height of the statue = h

we get

`(h)/(5.5) = 4\\\\h = 4 * 5.5\\\\h = 22\\\\`

Answer (c) height of statue = 22 meters