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
Now, According to question
From figure
In Δ AOB
Tan angle = [tex]\dfrac{\textrm perpendicular}{\textrm base}[/tex]
Or, Tan 35° = [tex]\dfrac{\textrm AB}{\textrm OA}[/tex]
Or, Tan 35° = [tex]\dfrac{\textrm h}{\textrm 100 feet}[/tex]
Or, 0.7002 = [tex]\dfrac{\textrm h}{\textrm 100 feet}[/tex]
∴ 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 = [tex]\dfrac{\textrm perpendicular}{\textrm base}[/tex]
Or, Tan 53° = [tex]\dfrac{\textrm AC}{\textrm OA}[/tex]
Or, Tan 53° = [tex]\dfrac{\textrm H}{\textrm 100 feet}[/tex]
Or, 1.3270 = [tex]\dfrac{\textrm H}{\textrm 100 feet}[/tex]
∴ 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
