Answer: The height of the pole is 175.97 ( approx )
Step-by-step explanation:
Let the height of the pole is x cm,
Also, let the angle of elevation of the sun to the pole at 3 pm is [tex]\theta[/tex]
Thus, by the question,
[tex]tan\theta = \frac{\text{ The height of the pole}}{\text{ The height of the shadow}}[/tex]
[tex]\implies tan\theta = \frac{x}{x}[/tex] ( at 3pm the height of shadow = height of the pole)
[tex]\implies tan\theta = 1[/tex]
[tex]\implies \theta = 45^{\circ}[/tex]
Again, according to the question,
When the angle of elevation is [tex](\theta - 12^{\circ})[/tex],
The height of shadow = x + 95,
[tex]\implies tan(45-12)^{\circ}=\frac{x}{x+95}[/tex]
[tex]\implies tan 33^{\circ}=\frac{x}{x+95}[/tex]
[tex]\implies tan 33^{\circ}x + 95\times tan33^{\circ}=x[/tex]
[tex]\implies tan 33^{\circ}x - x = - 95\times tan33^{\circ}[/tex]
[tex]\implies -0.3505924068 x = - 61.6937213538[/tex]
[tex]x=175.969930202\approx 175.97\text{ cm}[/tex]
