An airplane is sighted at the same time by two ground observ

An airplane is sighted at the same time by two ground observers who are 5 miles apart and both directly west of the airplane. They report the angles of elevation as 14 degree and 23 degree. How high is the airplane? Round to the nearest hundredth of a mile. 1.95 mi 3.02 mi 4.88 mi 1.21 mi

Solution

Let the height of the plane be h

tan 23=h/x

x is the distance of the first observer

h=x tan23

h=(x+5)tan14

xtan 23=(x+5)tan14

x=7.12

h=x tan 23=7.11tan 23=3.02miles