Question 1191760
Cj needs to know the width of a river.
 He climbs a tree 10 meters high above the ground and finds that the angle of depression of the two opposite banks of the river is 40° and 15°, respectively.
 How wide is the river?
:
One way to do this is to solve two right triangles.
The larger triangle is formed by top of the tree and the distance from the base of the tree to the furthest bank.
The angle of depression of 15 degrees, gives an interior angle of 75 at the top of the tree. (90-15)
the distance(a)from the tree to the far river bank is the side opposite
the tree is the side adjacent
tan(75) = {{{a/10)}}}
a = tan(75) * 10
a = 37.32 meters
:
The smaller triangle is formed by top of the tree and the distance from the base of the tree to the nearest bank.
The angle of depression of 40 degrees, gives an interior angle of 50 at the top of the tree.(90-40)
the distance (b) from the tree to the near river bank is the side opposite
the tree is the side adjacent
tan(50) = {{{b/10)}}}
b = tan(50) * 10
b = 11.92 meters
:
The width of the river then is: 37.32 - 11.92 = 25.4 meters