Answered By Emily H

To solve this problem you'll need to use the sine law to find the height of the triangle formed by the tower and the viewer's distance from its top and bottom:

$\frac{142}{\sin90}=\frac{h}{\sin23}$142sin90 =hsin23  

 $h=55.48$h=55.48m

Then, we can use Pythagorean theorem and quadratic formula to find the horizontal distance bewtween the base of the tower and its top:

 $142^2-55.48^2=\left(137-y\right)^2$142²−55.48²=(137−y)² 

  ^{$\sqrt{17085.97}=y^2-274y+18769$√17085.97=y2−274y+18769}  

 ^{$y^2-274y+18638.29=0$y2−274y+18638.29=0} 

  ^{$y=\frac{548-\sqrt{274^2-4\cdot18638.29}}{2}$y=548−√2742−4·18638.292}   

  ^{$y=6.29$y=6.29m}

^{Note that there is another possible solution to the quadratic equation ($y=267.8$y=267.8m), but we can ignore that as it doesn't make sence within the context of the problem.}

^{Finally, we can solve for $x$x with Pythagorean theorem:}

 ^{$x=\sqrt{55.48^2+6.29^2}$x=√55.482+6.292} 

 ^{$x=55.84$x=55.84m}