SOLUTION: At point A due east to the hut the angle of elevation is 45 degree and at point B due west to the hut the angle of elevation is 30 degree. If the distance of AB is 10 meter then fi

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Question 1185557: At point A due east to the hut the angle of elevation is 45 degree and at point B due west to the hut the angle of elevation is 30 degree. If the distance of AB is 10 meter then find the height of hut?
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
In triangle ACB angle B = 45 deg
tan 45 = 1 therefore AC =x
In triangle ADC angle D =60 deg
x/(10-x) = tan 60
x = 10*tan60 - tan 60 *x
x+tan 60x = 17.32
x(1+tan 60)= 17.32
x = 17.32/ (1+tan 60)

x = 6.34 m
.


Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
At point A due east to the hut the angle of elevation is 45 degree
and at point B due west to the hut the angle of elevation is 30 degree.
If the distance of AB is 10 meter then find the height of hut?
~~~~~~~~~~~~~~~~~~~~~~


        In the post by @mananth, the plot is incorrect - it is irrelevant to the problem.
        As a consequence, the entire solution in that post is incorrect.
        I came to bring a correct solution. 


Let D be the top of the hut.
Draw the perpendicular CD from D to the ground (point C is at the ground level).
Let x be the height of the hut, x = |CD|, which is unknown now.


Let A and B be the points at the ground level mentioned in the problem.


The height x of the triangle ADB is equal to AC:  x = AC  (since angle A is 45°).

Angle B is 30°, so  |BC| = .


From the other side,  |AC| + |BC| = 10 meters (given),  or

    x +  = 10.


It implies

     = 10,  x =  = 3.66 m  (rounded).


ANSWER.  The height of the hut is   = 3.66 m  (rounded).

Solved.



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