Question

Ares lies 46 feet from the base of the tower. Wonder woman stands on top of the tower. Ares angle of elevation to Wonder woman is 45°. How tall is the tower (in feet) if wonder woman is 6 feet tall?

Answer 1

The height of the tower is 40 feet .

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 =
`(\textrm perpendicular)/(\textrm base)`

Or, Tan Ф =
`(\textrm AC)/(\textrm OA)`

Or, Tan Ф =
`(\textrm AB + BC)/(\textrm OA)`

Or, Tan 45° =
`(\textrm H feet + h feet)/(\textrm d feet)`

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