We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
446
2
avatar

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?

 Aug 8, 2015

Best Answer 

 #2
avatar+27653 
+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)

.

 Aug 8, 2015
 #1
avatar
0

2.64953233737103 Km

 Aug 8, 2015
 #2
avatar+27653 
+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)

.

Alan Aug 8, 2015

23 Online Users

avatar