what number is half way between 73.7 and 73.71
Answers
Step-by-step explanation:
⟹h=a+x
\sf :\implies \red {x=\dfrac{2a\tan\alpha}{\tan\beta-\tan\alpha}}:⟹x=
tanβ−tanα
2atanα
⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀
\begin{gathered}\sf :\implies \purple { h=a+x}\\\\\end{gathered}
:⟹h=a+x
\begin{gathered} \sf :\implies h=a+\sf{ \dfrac{2a\tan\alpha}{\tan\beta-\tan\alpha}}\\\\\end{gathered}
:⟹h=a+
tanβ−tanα
2atanα
\begin{gathered}\sf :\implies h=\dfrac{a\tan\alpha+a\tan\beta}{\tan\beta-\tan\alpha}\\\\\end{gathered}
:⟹h=
tanβ−tanα
atanα+atanβ
\begin{gathered}\sf :\implies h=\dfrac{\left(\dfrac{a\sin\alpha}{\cos\alpha}+\dfrac{a\sin\beta}{\cos\beta}\right)}{\left(\dfrac{\sin\beta}{\cos\beta}-\dfrac{\sin\alpha}{\cos\alpha}\right)}\\\\\end{gathered}
:⟹h=
(
cosβ
sinβ
−
cosα
sinα
)
(
cosα
asinα
+
cosβ
asinβ
)
\begin{gathered}\sf :\implies h=\dfrac{\left(\dfrac{a\sin\alpha\cos\beta+a\cos\alpha\sin\beta}{\cos\alpha\cos\beta}\right)}{\left(\dfrac{\sin\beta\cos\alpha-\cos\beta\sin\alpha}{\cos\alpha\cos\beta}\right)}\\\\\end{gathered}
:⟹h=
(
cosαcosβ
sinβcosα−cosβsinα
)
(
cosαcosβ
asinαcosβ+acosαsinβ
)
\begin{gathered} \sf :\implies h=\dfrac{a(\sin\alpha\cos\beta+\cos\alpha\sin\beta)}{\sin\beta\cos\alpha-\cos\beta\sin\alpha}\\\\\end{gathered}
:⟹h=
sinβcosα−cosβsinα
a(sinαcosβ+cosαsinβ)
\begin{gathered}\sf{ :\implies \boxed{\underline\purple{{h=\dfrac{a\sin(\alpha+\beta)}{\sin(\beta-\alpha)}}}}}\\\\\end{gathered}
:⟹
h=
sin(β−α)
asin(α+β)