Suppose you live 5.2 miles from a hill. From your home you see a plane directly above the hill. Your angle of elevation to the plane is 27°. What is the plane’s altitude?

Guest Aug 8, 2015

#2**+10 **

tan(elevation) = altitude/horizontal distance, so:

tan(27°) = altitude/5.2miles

altitude = 5.2*tan(27°)

$${\mathtt{altitude}} = {\mathtt{5.2}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{27}}^\circ\right)} \Rightarrow {\mathtt{altitude}} = {\mathtt{2.649\: \!532\: \!337\: \!368\: \!8}}$$

altitude ≈ 2.6 miles (4.2 km)

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Alan Aug 8, 2015

#2**+10 **

Best Answer

tan(elevation) = altitude/horizontal distance, so:

tan(27°) = altitude/5.2miles

altitude = 5.2*tan(27°)

$${\mathtt{altitude}} = {\mathtt{5.2}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{27}}^\circ\right)} \Rightarrow {\mathtt{altitude}} = {\mathtt{2.649\: \!532\: \!337\: \!368\: \!8}}$$

altitude ≈ 2.6 miles (4.2 km)

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Alan Aug 8, 2015