Question

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

Answer 1

$\frac{ABsin\alpha sin\beta }{\sqrt{(si{n}^2\alpha -si{n}^2\beta )}}$ or $\frac{ABsin\alpha sin\beta }{\sqrt{\left[sin\right(\alpha +\beta \left)sin\right(\alpha -\beta \left)\right]}}$ or $\frac{ABtan\alpha tan\beta }{\sqrt{(ta{n}^2\alpha -ta{n}^2\beta )}}$

$AP=hcot\alpha ,BP=hcot\beta$

$B{P}^2=A{B}^2+A{P}^2$

$h^2(co{t}^2\beta -co{t}^2\alpha )=a^2$ Where AB = a

Now change to tan or sin and cosine etc.