Question

At a point to hundred feet from the base of the building, the angle of elevation to the bottom of the smokestack it’s 35°, and the angle of elevation to the top is 53°. Find the height of the smokestack

Answer 1

The height of the smokestack is 132.7 feet

Explanation:

Given as :

The distance of point to the base of building = d = 100 feet

The angle of elevation to bottom of smokestack = 35°

The angle of elevation to top of smokestack = 53°

Let The height of the building = h feet

Let The height of smokestack = H feet

Now, According to question

From figure

In Δ AOB

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

Or, Tan 35° =
`(\textrm AB)/(\textrm OA)`

Or, Tan 35° =
`(\textrm h)/(\textrm 100 feet)`

Or, 0.7002 =
`(\textrm h)/(\textrm 100 feet)`

∴ h = 0.7002 × 100

I.e h = 70.02 feet

So, The height of the building = h = 70.02 feet

Again

In Δ AOC

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

Or, Tan 53° =
`(\textrm AC)/(\textrm OA)`

Or, Tan 53° =
`(\textrm H)/(\textrm 100 feet)`

Or, 1.3270 =
`(\textrm H)/(\textrm 100 feet)`

∴ H = 1.3270 × 100

I.e H = 132.7 feet

So, The height of the smokestack = H = 132.7 feet

Hence, The height of the smokestack is 132.7 feet . Answer