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Published byRoderick Thornton Modified over 9 years ago
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Starter Write down a definition of the hypotenuse
Find the hypotenuse of the following triangles: 2cm 9cm 15cm 8cm 11cm 6cm
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Pythagoras’ Theorem Learning Objectives: Be able to find the hypotenuse using Pythagoras Be able to find the shorter side using Be able to apply your knowledge to worded problems
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Pythagoras’ Theorem c2 = a2 + b2 Square both the non-hypotenuse sides
Add the results together Square root your answer to find the length of the hypotenuse
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Pythagoras’ Theorem c2 = a2 + b2 c2 = c2 = c2 = 65 c =√65 c = 8.1 4 C 7
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Pythagoras’ Theorem We can use Pythagoras’ theorem to find the a shorter side by re-arranging the formula. c2 = a2 + b2 a2 = c2 – b2
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Pythagoras’ Theorem a2 = c2 – b2 a2 = 132 – 122 a2 = 169 – 144 a2 = 25 a = √25 a = 5 13cm 12cm a
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Pythagoras’ Theorem 6cm b 14cm
a2 = c2 – b2 a2 = 142 – 62 a2 = 196 – 36 a2 = 160 a = √160 a = 12.65 6cm b 14cm
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Pythagoras’ Theorem Find the length of the missing side 3m 25m
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Pythagoras’ Theorem 6cm 8.5cm
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Starter Find the length of the missing side.
6cm 15cm 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?
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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
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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?
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P
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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? 80km c2 = a2 + b2 c2 = c2 = c2 = 20800 c = √20800 c = km (2dp) 120km
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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?
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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
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The diagram shows a trapezium ABCD . Calculate the length of AB.
6.71cm 1 5cm This rectangle has a diagonal of 13cm and a width of 12cm. Calculate it’s height. 2 12.73m 3 A 8cm C c 9m 13cm 7cm j B D 9m 10cm 12cm Cardiff is 130 miles west of London. Hull is 200 miles north east of Cardiff. How far is Hull from London? miles 4 8.54m 5 16.52cm 6 Hull 8m d 23cm 200 miles 16cm Cardiff London 3m 130 miles f 13.23cm 7 8.94cm 8 6.93m 9 b k 20cm a 4m 8cm 8m 12cm 15cm
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CHECK YOUR ANSWERS AS YOU GO:
Your turn… CHECK YOUR ANSWERS AS YOU GO: Page 598 Exercise 26B, pages Q1, 2 (shorter sides) Exercise 26C, pages 555 – 557 Odd questions (worded problems) Exam Questions, pages 558 – 599 Q4 – 8 (mixed, past exam questions)
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