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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

### Best Answer

#2
+24983
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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

### 2+0 Answers

#1
+30088
+5

height = radius*tan(elevation)

radius = circumference /(2pi)

so radius = 29/(2pi) metres

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

height ≈ 7 metres

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Aug 9, 2015
#2
+24983
+5
Best Answer

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

heureka Aug 9, 2015