Answer:
The height of the tower is 40 feet .
Step-by-step explanation:
Given as :
The distance of Ares from the base of the tower = d = 46 feet
Wonder woman stands on top of the tower
The height of the wonder women = h = 6 feet
Angle of elevation to wonder women = Ф = 45°
Let The height of the tower = H feet
Now, From figure
Total height for the angle of elevation = H + h
Tan angle = [tex]\dfrac{\textrm perpendicular}{\textrm base}[/tex]
Or, Tan Ф = [tex]\dfrac{\textrm AC}{\textrm OA}[/tex]
Or, Tan Ф = [tex]\dfrac{\textrm AB + BC}{\textrm OA}[/tex]
Or, Tan 45° = [tex]\dfrac{\textrm H feet + h feet}{\textrm d feet}[/tex]
Or, d × Tan 45° = H + h
Or, 46 feet × 1 = H + 6 feet
∴ H = 46 feet - 6 feet
i.e H = 40 feet
So, The height of the tower = H = 40 feet
Hence, The height of the tower is 40 feet . Answer
