SOLUTION: The angles of elevation of the top Hof a vertical pole HO are observed to be e and a from points P and Q due east and due south of the post. If the distance PQ = d, show that the h
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Question 1205058: The angles of elevation of the top Hof a vertical pole HO are observed to be e and a from points P and Q due east and due south of the post. If the distance PQ = d, show that the height of the post is:
Found 3 solutions by ikleyn, mananth, math_tutor2020:Answer by ikleyn(52781) (Show Source):
You can put this solution on YOUR website! In right triangle POH , cot a = OP/OH
OH * cot a = OP
In right triangle QOH , cot b = OQ/OH
OQ= OH cot b
In right triangle POQ
OP^2+OQ^2= PQ^2
OH^2 * cot^2 a +OH^2cot^2b= PQ^2
OH^2 ( cot^2 a +cot^2b)= d^2 (given PQ=d)
OH^2= d^2/ ( cot^2 a +cot^2b)
You can put this solution on YOUR website!
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 red:
tan(alpha) = h/OA (it should be tan(alpha) = h/AP instead)
tan(beta) = h/OB (it should be tan(beta) = h/BP instead)
Since OAB is a right angled triangle (triangles OPA, OPB, and ABP are right triangles however)
The second to last line where it has h^2+cot^2(alpha) as part of it (it should be h^2*cot^2(alpha). Not sure where the plus sign came from).
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. pythagorean theorem
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