A jet plane is at a vertical height of h. The angles of depression of two tanks on the horizontal ground are found to have measures α and β,αβ. Prove that the distance between the tanks is tanα −tanβ h(tanα −tanβ ) assuming both the tanks are on the same side of the jet plane.

Question

A jet plane is at a vertical height of h. The angles of depression of two tanks on the horizontal ground are found to have measures α and β,α>β. Prove that the distance between the tanks is tanα −tanβ  h(tanα −tanβ  ) ​ assuming both the tanks are on the same side of the jet plane.

Filo · Accepted Answer

Let A be the position of the jet plane and C,D be the two tanks on the same side of the jet planeHere B=hBC= distance between base and 1st tank =yCD= distance between two tanks =xIn △ABCtanα =BCAB​∴tanα =yh​∴y=tanα  h​...(1)In △ABDtanβ =BDAB​∴tanβ =x+yh​∴x+y=tanβ  h​....(2)From (1) and (2)x+tanα  h​=tanβ  h​⇒x=tanβ  h​−tanα  h​⇒x=tanα tanβ  h(tanα −tanβ )​Hence the distance between the two tanks is tanα tanβ  h(tanα −tanβ )​

Question Text	A jet plane is at a vertical height of $h$ . The angles of depression of two tanks on the horizontal ground are found to have measures $α$ and $β, α > β$ . Prove that the distance between the tanks is $\frac{h ( tan α - tan β )}{tan α - tan β}$ assuming both the tanks are on the same side of the jet plane.
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Text solutionVerified

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A jet plane is at a vertical height of h. The angles of depression of two tanks on the horizontal ground are found to have measures α and β,α>β. Prove that the distance between the tanks is tanα −tanβ h(tanα −tanβ ) ​ assuming both the tanks are on the same side of the jet plane.

Text solutionVerified

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