Question
An airplane is sighted at the same time by two ground observers who are 2 miles apart and both directly west of the airplane. They report the angles of elevation as 11˚ and 20˚. How high is the airplane? Round to the nearest hundredth of a mile.
Answers
make your sketch
drop an altitude from the plane to the ground to get 2 right-angled triangles
let the height of the plane be h
let the base of the 11° triangle be x
then the base of the other triangle is 2-x
from the 11° triangle:
tan11 = h/x --->h = xtan11
from the other triangle:
tan20 = h/(2-x) --> h = (2-x)tan20
xtan11 = (2-x)tan20
xtan11 = 2 - xtan20
xtan11 + xtan20 = 2
x(tan11 + tan20) = 2
x = 2/(tan11 + tan20)
h = x tan11
= 2tan11/(tan11 + tan20)
= ...
only now would I go to my calculator to do the evaluation.
drop an altitude from the plane to the ground to get 2 right-angled triangles
let the height of the plane be h
let the base of the 11° triangle be x
then the base of the other triangle is 2-x
from the 11° triangle:
tan11 = h/x --->h = xtan11
from the other triangle:
tan20 = h/(2-x) --> h = (2-x)tan20
xtan11 = (2-x)tan20
xtan11 = 2 - xtan20
xtan11 + xtan20 = 2
x(tan11 + tan20) = 2
x = 2/(tan11 + tan20)
h = x tan11
= 2tan11/(tan11 + tan20)
= ...
only now would I go to my calculator to do the evaluation.
an airplane is sighted at the same time by two ground observers who are 4 miles apart and are both directly west of the airplane. They report the angles of elevation as 11 and 22. What is the altitude of the airplane? Round to the nearest tenth
1.67 miles
Related Questions
Two observers 1 km apart spot an airplane. The angles of elevation of the airplane from the two obs...
An airplane is 34 ground miles from the end of the runway and 6 miles high when it begins its approa...
From the top of the control tower 250 m tall, an airplane is sighted on the ground below. If the air...
A person flying in an airplane 2 miles off the ground spots a car on the ground 3 miles ahead of him...