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3 years ago

6

HELP PLEASE!! As John walks 16 ft towards a chimney, the angle of elevation from his eye to the top of the chimney changes from

30° to 45°. Identify the height of the chimney from John's eye level to the top of the chimney rounded to the nearest foot.

1 answer:

rjkz [21]3 years ago

6 0

Answer: 22 feet.

Step-by-step explanation:

Note that there are two right triangles in the figure attached: ACD and BCD. Where "h" is the height of the chimeney from John's eye level to the top of the chimney.

You need to use the trigonometric identity $tan\alpha=\frac{opposite}{adjacent}$ for this exercise.

For the triangle BCD:

$tan(45\°)=\frac{h}{x}$

Solve for h:

$h=xtan(45\°)\\h=x$

For the triangle ACD:

$tan(30\°)=\frac{h}{x+16}$

Substitute $h=x$ and solve for h:

$tan(30\°)=\frac{h}{h+16}\\\\(h+16)(tan(30\°))=h\\\\0.577h+9.237=h\\\\9.237=h-0.577h\\\\9.237=0.423h\\\\h=\frac{9.237}{0.423}\\\\h=21.836ft$

Rounded to the nearest foot:

$h=22ft$

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