The figure *ABCD* is a square with side length *a + b*, and
it consists of the four congruent right-angled triangles and a square, *EFGH*,
with side length *c*.
This proof was devised by the Indian mathematician, Bhaskara, in 1150
AD.
Applications of Pythagoras' Theorem
To solve a word problem, read the problem and draw a diagram. Then
write the given information on the diagram and identify any right-angled
triangle(s). Use Pythagoras' Theorem to form an equation and solve
the equation thus obtained. Translate the solution into a worded
answer.
#### Example 1
A ship sails 80 km due east and then 18 km due north. How far is the
ship from its starting position when it completes this voyage?
##### Solution:
Let the distance of the ship from its starting point be *x* km. We
can draw a diagram of the ship's voyage on a set of axes, with the
horizontal axis representing east and the vertical axis representing
north. The ship is at the point *P* and it started at the origin.
There is a right angle at *A*.
By Pythagoras' Theorem from triangle *OAP*,
Example 2
A ladder 7.25 m long stands on level ground so that the top end of the
ladder just reaches the top of a wall 5 m high. How far is the foot of the
ladder from the wall?
##### Solution:
Let the distance from the foot of the ladder to the base of the wall be *x* m.
By Pythagoras' Theorem and the diagram,
**
**
So, the distance from the foot of the ladder to the wall is 5.25 m.
Using a Construction Line
Sometimes we need to draw a construction line (shown as a broken line)
in the diagram to form a right-angled triangle.
#### Example 3
Use the information given in the following diagram to find the value of *x*.
##### Solution:
Join *BD* by a broken line to form the right-angled triangles *ABD* and *BCD*. Let *BD* = *y* cm. |