Fill in the blanksThe angle of elevation of a tower at a place A due south it is - and at a place due west of A and at a distance a from it- the elevation is - the height of tower is -

AB sin α sin β√((sin^2 α #160; sin^2 β)) or AB sin α sin β√([sin ( α + β) sin ( α β)]) or AB tan α tan β√((tan^2 α #160; tan^2 β)) ...

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Standard X

Mathematics

Standard Values of Trigonometric Ratios

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Question

Fill in the blanks
The angle of elevation of a tower at a place $A$ due south it is $θ$ and at a place due west of $A$ and at a distance $a$ from it, the elevation is $ϕ$ , the height of tower is ____________.

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Solution

$\frac{A B s i n α s i n β}{\sqrt{(s i n^{2} α - s i n^{2} β)}}$ or $\frac{A B s i n α s i n β}{\sqrt{[s i n (α + β) s i n (α - β)]}}$ or $\frac{A B t a n α t a n β}{\sqrt{(t a n^{2} α - t a n^{2} β)}}$
$A P = h c o t α, B P = h c o t β$
$B P^{2} = A B^{2} + A P^{2}$
$h^{2} (c o t^{2} β - c o t^{2} α) = a^{2}$ Where AB = a
Now change to tan or sin and cosine etc.

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Similar questions

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Fill in the blanksThe angle of elevation of a tower at a place A due south it is θ and at a place due west of A and at a distance a from it, the elevation is ϕ, the height of tower is ____________.

ABsinαsinβ√(sin2α−sin2β) or ABsinαsinβ√[sin(α+β)sin(α−β)] or ABtanαtanβ√(tan2α−tan2β)AP=hcotα,BP=hcotβBP2=AB2+AP2h2(cot2β−cot2α)=a2 Where AB = aNow change to tan or sin and cosine etc.

Fill in the blanks
The angle of elevation of a tower at a place $A$ due south it is $θ$ and at a place due west of $A$ and at a distance $a$ from it, the elevation is $ϕ$ , the height of tower is ____________.