Answer:
214 ft
Step-by-step explanation:
Height of building = 94.9 ft
The angle of elevation of the top of the flagpole = θ₁ = 35.3°
The angle of elevation of the bottom of the flagpole = θ₂ = 26.2°
Let,
Height of building = x
Distance from observation point to base of building = y
[tex]tan 26.2 =\frac{x}{y}\\\Rightarrow y=\frac{x}{tan26.2}[/tex]
[tex]tan 35.3 =\frac{94.9+x}{y}\\\Rightarrow tan 35.3 =\frac{94.9+x}{\frac{x}{tan26.2}}\\\Rightarrow \frac{x}{tan26.2}tan35.3=94.9+x\\\Rightarrow \frac{tan35.3}{tan26.2}x-x=94.9\\\Rightarrow x=\frac{94.9}{\frac{tan35.3}{tan26.2}-1}\\\Rightarrow x=214.84/ ft[/tex]
I have used the exact values from the calculator.
∴ Height of the building is 214.84 ft
Answer:
The height of the building is 214.84 ft.
Step-by-step explanation:
Given information:
The height of the flagpole = 94.9 ft.
The angle of elevation of top = θ[tex]_1[/tex] = [tex]35.3^o[/tex]
The angle of elevation of bottom = θ[tex]_2=26.2^o[/tex]
If the height of building is [tex]x[/tex]
Then,
[tex]tan 26.2=x/y\\y=x/(tan26.2)\\[/tex]
And:
[tex]tan 35.3=(94.9+x)/y\\[/tex]
[tex]94.9+x=y \times tan35.3[/tex]
On putting the value in above equation:
[tex]x=\frac{94.9}{\frac{tan35.3}{tan26.2}-1 }[/tex]
solving the above equation:
[tex]x=214.84 ft.[/tex]
Hence, the height of the building is 214.84 ft.
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