a right-angled triangle

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Presentation transcript:

a right-angled triangle Objective: calculating a missing length on a right-angled triangle: Pythagoras’ Theorem two sides are given and you will work out one length a scalene triangle a right-angled triangle Question What is the length of a side for each of the squares below? Area = 85cm2 Area = 36cm2 16cm2

a c c a b b a b c c b a a b c b c a hypotenuse Objective: calculating a missing length on a right-angled triangle: Pythagoras’ Theorem hypotenuse right-angle opposite longest length a c c a b b a b c hypotenuse c b a a b c b c a

Objective: calculating a missing length on a right-angled triangle: Pythagoras’ Theorem Interesting fact: The iPad has a 25cm screen, this means that it’s diagonal length is 25cm. For all screens like computers, iPads, televisions, iPhones etc. the length quoted is always the diagonal length as this is always the longest.

Objective: calculating a missing length on a right-angled triangle: Pythagoras’ Theorem 169 25 144

Objective: calculating a missing length on a right-angled triangle: Pythagoras’ Theorem 8cm 15cm 5cm 12cm 7cm 15cm

9cm 15cm ???cm 5cm 12cm ???cm ???cm ???cm 12cm 5cm 15cm 9cm Objective: calculating a missing length on a right-angled triangle: Pythagoras’ Theorem ???cm ???cm 12cm 5cm 9cm 15cm 5cm 9cm ???cm 15cm 12cm ???cm

Objective: calculating a missing length on a right-angled triangle: Pythagoras’ Theorem Imagine the squares click once to play 12cm 5cm 52 x2 122 12cm 5cm ???cm 5cm 12cm Write down your calculation x2 + 52 = 122 Then take square roots to give the value of x Look at your calculation and work through it x = √119 x2 + 25 = 144 = 144−25 = 119 x = 10.91cm x2

Objective: calculating a missing length on a right-angled triangle: Pythagoras’ Theorem Example 1 Work out the height of the trapezium, can you work out the area? 5.7cm 5.5cm 2.8cm why? 5.5cm 2.9cm 2.9cm

Example 2 Work out the distance between the points (1,1) and (14,6) Objective: calculating a missing length on a right-angled triangle: Pythagoras’ Theorem Example 2 Work out the distance between the points (1,1) and (14,6)

5 3 4 The regulation for safe use of ladders states that: Objective: calculating a missing length on a right-angled triangle: Pythagoras’ Theorem Functional Maths Pythagoras is used in real life and even as far back as Egyptian times (before Pythagoras), labourers used a trick to create a right angle. The regulation for safe use of ladders states that: the foot of a 6 m ladder must be placed between 1.3 m and 2.2 m from the foot of the wall. What is the maximum height the ladder can safely reach up the wall? 5 3 4 To make a right-angle, which was needed to construct Pyramids Egyptians used a rope divided in the ratio 3:4:5 which made a right-angle when tied around three posts.