(英文)數學一問!!! 1 0分

There vertical poles A, B and C . The heights of poles A and B are 5m and 7m respectively. Pole A is 3m from Pole Band 9m from Pole C. the top of the three poles are in a straight line. Find the height of Pole C
LET THE straight line call ABC
then the slope of ABC
= the slope of AB
=2/3
ALSO
the slope of ABC
= the slope of BC
=(X-7)/6 (where X is the height of Pole c)
SO
(X-7)/6=2/3
X=11
the height of Pole c is 11m

Height of A =5m
Height of B =7m
Let height of C = xm
A...B....C
.............|
.....|.......|
|....|......|
|....|......|
..3..
.......9......
Gradient of AB
= (Height of B - height of A ) / distance A from B
= (7 - 5)/3 = 2/3
Gradient of AC
= (Height of C - height of A ) / distance A from C
= (x-3)/9
Since three poles are in a straight line,
Gradient of AB = Gradient of AC
2/3 = (x-3)/9
2/3 * 9 = x - 3
6 = x-3
x = 9
The height of Pole C is 9m.