Answer:
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
<u>Now, According to question</u>
From figure
<u>In Δ AOB</u>
Tan angle = ![\dfrac{\textrm perpendicular}{\textrm base}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctextrm%20perpendicular%7D%7B%5Ctextrm%20base%7D)
Or, Tan 35° = ![\dfrac{\textrm AB}{\textrm OA}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctextrm%20AB%7D%7B%5Ctextrm%20OA%7D)
Or, Tan 35° = ![\dfrac{\textrm h}{\textrm 100 feet}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctextrm%20h%7D%7B%5Ctextrm%20100%20feet%7D)
Or, 0.7002 = ![\dfrac{\textrm h}{\textrm 100 feet}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctextrm%20h%7D%7B%5Ctextrm%20100%20feet%7D)
∴ h = 0.7002 × 100
I.e h = 70.02 feet
So, The height of the building = h = 70.02 feet
Again
<u>In Δ AOC</u>
Tan angle = ![\dfrac{\textrm perpendicular}{\textrm base}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctextrm%20perpendicular%7D%7B%5Ctextrm%20base%7D)
Or, Tan 53° = ![\dfrac{\textrm AC}{\textrm OA}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctextrm%20AC%7D%7B%5Ctextrm%20OA%7D)
Or, Tan 53° = ![\dfrac{\textrm H}{\textrm 100 feet}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctextrm%20H%7D%7B%5Ctextrm%20100%20feet%7D)
Or, 1.3270 = ![\dfrac{\textrm H}{\textrm 100 feet}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctextrm%20H%7D%7B%5Ctextrm%20100%20feet%7D)
∴ 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