Question 1105445: an adult and a young boy, standing on the ground are one metre apart .the height of the adult is 2 times the height of young boy. if at the mid-point of the line joining their feet the angular elevation of their tops are complementary , find the height of the young boy
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! A very, very small adult!
Let  be the height of the boy, in metres.
If the man and boy are standing on level ground,
their heights can be represented as vertical lines,
perpendicular to the horizontal ground.
The sketch below shows the two humans' heights,
the ground under them,
and the line segments connecting point M
(the mid-point of the line joining their feet)
to the top of their heights.
 The red and green arcs show the angles of elevation from M to the top of the adult's and boy's heads.
Those two angles are complementary,
meaning that their measures add up to  or  .
As the two triangles are right triangles,
the acute angles in each triangle are also complementary,
meaning that their measures add up to or .
As a consequence, for each triangle, the angle not marked with an arc
is complementary to the marked angle in the other triangle.
That makes the triangles similar.
Similar triangles have proportional side lengths.
With side length measured in m,
 
That would make the height of the boy  ,
and the height of the adult would be  .
That would make that adult a very strong contender for the title of shortest man (or woman) alive.
|
|
|
