Question 1153642: The angle of elevation of the top of a flag post from a point A on level ground is 13 degrees.The angle of elevation of elevation of the top of the flag post from another point B nearer the flag post and 120 m from A is 30 degrees. B is between A and the bottom of the flag post and the three points are collinear. Find:
( a)the distance from the point B to the top of the flag post.
(b)the height of the flag post.
Answer by Cromlix(4381)   (Show Source):
You can put this solution on YOUR website! Hi,
First draw a right angled triangle CDB.
CD will represent the flagpole (C at the top and D at the base.)
DB will represent the length of ground between the base of the flagpole (D) and the point B
Angle CDB will equal 30 degrees (given)
Now, extend base line DB out and put an A at the end.
Draw another line from the top of the flagpole C to A. This will form a second right angled triangle CDA.
Angle CAD will equal 13 degrees (given)
Now add angle CBA which is 180 - 30 deg. = 150 deg. (DA is a straight line)
By deduction angle BCA = 180 -(150 + 30 deg) = 17 deg
Consider triangle CBA
Angle CAB = 13 deg, Angle CBA = 150 deg and Angle BCA = 17 deg.
Using Sine Rule (a/Sin A = b/Sin b = c/Sin C)
a/Sin A = c/Sinc
a/sin13 = 120m/sin17
Cross multiply
a * sin17 = 120 * sin 13 (* means times)
a = (120 x sin13)/sin 17
a = 92.3 m
This is the distance from the point B to the top of the flagpost.
Now consider triangle CDB
Side CB = 92.3 m (the Hypotenuse)
Angle DBC = 30 deg
Using Trig Ratios (Sin = Opposite/Hypotenuse, Cos = Adjacent/ Hypotenuse and Tan = Opposite/Adjacent
The height of the flagpost.(CD)
sin30 = CD/CB
sin30 = CD/92.3
Cross multiply
CD = sin30 * 92.3
CD = 46.2 m (1 decimal place)
Sorry its so long winded, but I hope it helps. :-)
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