Answer:
The height of the wall is 52.2 feet.
Step-by-step explanation:
Given:
From the figure shown, HT is the height of Carlos, 'V' is the position of mirror.
So, TV = 4 ft, VS = 36 ft, HT = 5.8 ft.
Let the height of the wall be 'x'. So, JS = 'x'
Now, consider the two triangles HTV and JVS
Statements Reasons
1. ∠ HTV ≅ ∠ JSV Right angles are congruent
2. ∠ HVT ≅ ∠ JVS Given in the figure
Therefore, ΔHTV and Δ JVS are similar triangles by AA postulate.
Now, from definition of similar triangles, corresponding sides of two similar triangles are in proportion to each other. Therefore,
![\frac{HT}{JS}=\frac{TV}{VS}=\frac{HV}{JV}](https://tex.z-dn.net/?f=%5Cfrac%7BHT%7D%7BJS%7D%3D%5Cfrac%7BTV%7D%7BVS%7D%3D%5Cfrac%7BHV%7D%7BJV%7D)
Considering the first two pair of fractions, we have:
![\frac{5.8}{x}=\frac{4}{36}\\\\36\times 5.8=4\times x\\\\x=\frac{36\times 5.8}{4}\\\\x=9\times 5.8=52.2\ ft](https://tex.z-dn.net/?f=%5Cfrac%7B5.8%7D%7Bx%7D%3D%5Cfrac%7B4%7D%7B36%7D%5C%5C%5C%5C36%5Ctimes%205.8%3D4%5Ctimes%20x%5C%5C%5C%5Cx%3D%5Cfrac%7B36%5Ctimes%205.8%7D%7B4%7D%5C%5C%5C%5Cx%3D9%5Ctimes%205.8%3D52.2%5C%20ft)
Therefore, the height of the wall is 52.2 feet.