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 15
A ladder 5.8 m long stands on level ground and its top just reaches the
top of a wall 4.1 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 of the foot of the ladder from the wall is 4.1 m.
Example 16
A square schoolyard has sides 47 m long. Find:
a. the distance from one corner to the opposite corner correct to the
nearest metre.
b. how much further you would walk if you had to follow a path along
two sides instead of 'cutting' across.
Solution:
So, the length of the diagonal is 66 m (to the nearest metre).
b. The path along the two sides covers a distance of 94 m, and
this is 94 – 66 = 28 metres longer than going straight across.
Navigation Problem
Example 17
A ship sails 42 km due east and then 25 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,
So, the ship is 48.88 km from the starting point.
Example 18
The length of the diagonal of a rectangular paddock is 61 m and the
length of one side is 60 m. Find:
a. the width of the paddock
b. the length of the fencing needed to enclose the paddock
Solution:
So, the width of the paddock is 11 m.
So, the length of the fence required to enclose the paddock is 142 m.
