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)
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?
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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).
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