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# 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

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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?

Aug 9, 2015

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$$c=2\pi r=29 \\\\ h=r\cdot \tan{(57)}\\\\ h=\dfrac{29}{2\pi}\cdot\tan {(57)}\qquad r=4.62 ~m \\\\ h=4.61549335\cdot 1.539864964\\\\ h=7.1072365~m\\\\ h = 7.11~m$$

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Aug 9, 2015

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

height ≈ 7 metres

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Aug 9, 2015
#2
+5
$$c=2\pi r=29 \\\\ h=r\cdot \tan{(57)}\\\\ h=\dfrac{29}{2\pi}\cdot\tan {(57)}\qquad r=4.62 ~m \\\\ h=4.61549335\cdot 1.539864964\\\\ h=7.1072365~m\\\\ h = 7.11~m$$