Question

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.

Answer 1

ANSWER

The height is $22ft$


EXPLANATION

Let the height of the chimney be x.

$\tan(45 \degree) = \frac{x}{y}$

$1 = \frac{x}{y}$

$x = y$

$\tan(30 \degree) = \frac{x}{16+ y}$

$\frac{ \sqrt{3} }{3} = \frac{x}{16 + y}$

Cross multiply

$\sqrt{3} (16 + y) = 3x$

$16 \sqrt{3} + y \sqrt{3} = 3x$

Put

$y = x$

into the equation;

$16 \sqrt{3} + x \sqrt{3} = 3x$

Group similar terms:

$16 \sqrt{3}= 3x - x \sqrt{3}$

$16 \sqrt{3}= (3 - \sqrt{3})x$

$\frac{16 \sqrt{3} }{3 - \sqrt{3} } = x$



$x=21.856$


The height of the chimney to the nearest feet is 22