Let A,B be mountain peaks
C be helicopter’s location
let B be such a point that:
ADis the distance between the mountain peaks
BDis the difference in height between mountain peaks
∠BDA=90°
∠CAD=90°
from the conditions of the problem
∠BAD=18°
∠ACB=43°
CA=1000
find angles
α=∠CAB=∠CAD−∠BAD=90°−18°=72°
γ=∠ACB=43∘
β=∠CBA=180°−∠CAB−∠BCA=
180°−(72°+43°)=65°
by the sine theorem △ABC
sinγAB=sinβAC
AB=sinβACsinγ
from △ABD
BD=AB∗sin∠BAD=sinβACsinγ∗sin∠BAD
BD=sin65°1000sin43°sin18°≈ 232.5
AD=AB∗cos∠BAD=sinβACsinγ∗cos∠BAD
AD=sin65°1000sin43°cos18°≈715.7
then the height of the highest mountain peak
h=BD+5210=232.5+5210=5442.5 ft
Answer: 715.7 ft distance between mountain peaks
5442.5 ft the height of the highest mountain peak
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