Question 1205058
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The toppr link that tutor ikleyn posted is riddled with errors. 
It's shocking how professors on the toppr website have "verified" that solution.
I can possibly understand that ikleyn may have glossed over those errors, but she should be more careful next time.


Here are the errors marked in <font color=red>red</font>:<ul><li><font color=red>tan(alpha) = h/OA</font> (it should be tan(alpha) = h/AP instead)</li><li><font color=red>tan(beta) = h/OB</font> (it should be tan(beta) = h/BP instead)</li><li><font color=red>Since OAB is a right angled triangle</font> (triangles OPA, OPB, and ABP are right triangles however)</li><li><font color=red>The second to last line where it has h^2+cot^2(alpha) as part of it</font> (it should be h^2*cot^2(alpha). Not sure where the plus sign came from).</li></ul>
Here's what it should say
tan(alpha) = h/AP ---> AP = h*cot(alpha)
tan(beta) = h/BP ----> BP = h*cot(beta)


Then focus on right triangle ABP that is flat on the ground.
{{{(AB)^2 = (AP)^2 + (BP)^2}}} pythagorean theorem


{{{d^2 = (h*cot(alpha))^2 + (h*cot(beta))^2}}}


{{{d^2 = h^2*cot^2(alpha) + h^2*cot^2(beta)}}} 


{{{d^2 = h^2*( cot^2(alpha) + cot^2(beta) )}}}


{{{h^2 = (d^2)/( cot^2(alpha) + cot^2(beta) )}}}


{{{h = sqrt( (d^2)/( cot^2(alpha) + cot^2(beta) ) )}}}


{{{h =  (sqrt(d^2))/( sqrt(cot^2(alpha) + cot^2(beta) ) )}}}


{{{h =  d/( sqrt(cot^2(alpha) + cot^2(beta) ) )}}} since d > 0
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