starter a)write down a definition of the hypotenuse b)find the hypotenuse of the following...
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Starter
a) Write down a definition of the hypotenuse
b) Find the hypotenuse of the following triangles:
8cm
6cm
15cm
2cm9cm
11cm
Pythagoras’ Theorem
Learning Objectives:
Be able to find the hypotenuse using Pythagoras Be able to find the shorter side using Pythagoras Be able to apply your knowledge to worded problems
Pythagoras’ Theorem
• c2 = a2 + b2
1.Square both the non-hypotenuse sides2.Add the results together3.Square root your answer to find the length of
the hypotenuse
Pythagoras’ Theorem
c2 = a2 + b2
c2 = 42 + 72
c2 = 16 + 49c2 = 65c =√65c = 8.14
7
C
Pythagoras’ Theorem
• We can use Pythagoras’ theorem to find the a shorter side by re-arranging the formula.
• c2 = a2 + b2
• a2 = c2 – b2
Pythagoras’ Theorem
a2 = c2 – b2
a2 = 132 – 122
a2 = 169 – 144a2 = 25a = √25a = 5
12cm
a
13cm
Pythagoras’ Theorem
a2 = c2 – b2
a2 = 142 – 62
a2 = 196 – 36a2 = 160a = √160a = 12.65
6cm
14cm b
Pythagoras’ Theorem
• Find the length of the missing side
3m25m
Pythagoras’ Theorem
8.5cm
6cm
Starter• Find the length of the missing side.
6cm15cm
2m
24m
A ladder is leaning against a wall. It reaches 9m up the wall, and is 12m long. How far from the wall is the ladder standing?
Practical Problems• When using Pythagoras’ theorem to solve
practical problems, draw a right-angled triangle to represent the problem– Identify the unknown variable by reading what the
questions is asking– Identifying the known values and substitute these
into Pythagoras’ theorem– Solve for the unknown value– Use the result to write the answer as a complete
sentence
Pythagoras’ Theorem
• A ladder is leaning against a wall. It reaches 9m up the wall, and is 12m long. How far from the wall is the ladder standing?
Pythagoras’ Theorem• A plane flies 120km due north, and then heads
due east for 80km. How far is the plane from it’s starting point?
120km
80kmc2 = a2 + b2
c2 = 1202 + 802
c2 = 14400 + 6400c2 = 20800c = √20800c = 144.22km (2dp)
Pythagoras’ Theorem
• The size of TV screens are measured by the diagonal distance from corner to corner. A 46” screen has a height of 30”. How wide is the screen?
Have I Got Hypotenuse For You
Rules:
• Select a number• Answer the question – find the
length of the hypotenuse• You have 1 minute• If you get it wrong, it passes
over to the other team
6.71cm
16.52cm8.54m151.99 miles
12.73m5cm
6.93m8.94cm13.23cm
The diagram shows a trapezium ABCD . Calculate the length of AB.
Cardiff is 130 miles west of London. Hull is 200 miles north east of Cardiff.
How far is Hull from London?
This rectangle has a diagonal of 13cm and a width of 12cm.
Calculate it’s height.
12cm 8cm
b
3m
8m d
9m
9m
23cm16cm
f
c
k
4m8m
15cm
a
10cm
7cm
8cmA
D
C
B
20cm
130 miles
200 miles
Cardiff London
Hull
j
12cm
13cm
65
3
98
1 2
4
7
Your turn…
• Exercise 26B, pages 553-554 – Q1, 2 (shorter sides)
• Exercise 26C, pages 555 – 557 – Odd questions (worded problems)
• Exam Questions, pages 558 – 599– Q4 – 8 (mixed, past exam questions)
CHECK YOUR ANSWERS AS
YOU GO:Page 598
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