A high fountain of water is located at the center of a circular pool. Circumference is 29.0 meters. Angle of elevation of the bottom of the fountain is 57 degrees. How high is the fountain?

Guest Aug 9, 2015

#1**+5 **

height = radius*tan(elevation)

radius = circumference /(2pi)

so radius = 29/(2pi) metres

$${\mathtt{height}} = {\frac{{\mathtt{29}}}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{\pi}}\right)}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{57}}^\circ\right)} \Rightarrow {\mathtt{height}} = {\mathtt{7.107\: \!236\: \!499\: \!870\: \!214\: \!1}}$$

height ≈ 7 metres

.

Alan
Aug 9, 2015