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

The height of the smokestack is 132.7 feet

Step-by-step 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 =

Or, Tan 35° =  

Or, Tan 35° =  

Or, 0.7002 =  

∴  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 =

Or, Tan 53° =  

Or, Tan 53° =  

Or, 1.3270 =  

∴  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

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step-by-step explanation: