Providing a figure for given problem

Question

The Question is from Challenge and Thrill of Pre College Mathematics, Ex. 6.10 ques no. 8

I've been trying this ques for a lot of time but I've been facing the following problems

How can two points(at each end of base) extend the same angle of elevation. If they do their respective line of sight will never meet

Secondly if there is a typing error and it should be that the peak subtends an angle then the problem is how can a point subtend an angle.

Any hint or a figure of the given problem would suffice.

The Question is also present in the link below. It is ques number 4

https://www.google.com/amp/s/madhavamathcompetition.com/2016/07/10/heights-and-distances-ii-problems-for-rmo-and-iitjee-maths/amp/

Or the photo here

https://ibb.co/Cbs2BwX

Answer 1

Problem #4 solution
Let midpoint of $AB$ be $O$.

In right triangle $PON$ we have $ON = \dfrac{PN}{\tan\phi}$
In right triangle $PAN$ we have $AN = \dfrac{PN}{\tan\theta}$

Finally in right triangle $AON$ apply pythagoras : $$\begin{align} &OA^2+ON^2 = AN^2\\ &a^2+\dfrac{PN^2}{\tan^2\phi} = \dfrac{PN^2}{\tan^2\theta}\\ \end{align}$$

Isolate $PN$ and simplify.

Answer 2

Here is a picture to better understand the problem #3.

$PN$ is the vertical tower.
$N, A, B$ are on the ground on the same plane.
$PN\perp NA \perp AB$
$\angle PAN =\alpha$
$\angle PBN = \beta$

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You want to show $$PN = AB\dfrac{\sin\alpha\sin\beta}{\sqrt{\sin(\alpha+\beta)\sin(\alpha-\beta)}}$$