19 March 2022 LO: To use Pythagoras theorem in right-angled triangles. Problem solving using Pythagoras Theorem Solving problems using Pythagoras Theorem Pythagoras Theorem can be used to solve many problems involving the lengths in
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19 March 2022 LO: To use Pythagoras’ theorem in right-angled triangles. Problem solving using Pythagoras’ Theorem<br>
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Solving problems using Pythagoras’ Theorem Pythagoras’ Theorem can be used to solve many problems involving the lengths in right-angled triangles. When solving a problem using Pythagoras’ Theorem always do the following: State Pythagoras’ Theorem for the given side lengths before substituting any values. Draw a clearly labelled diagram of the situation. Make sure that your answer is sensible given the lengths of the other two sides. Write your answer in sentence form Mark on known lengths and right angles. Use a symbol to represent the unknown length. Solve the equation.<br>
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Finding the lengths of diagonals Pythagoras’ Theorem has many applications. For example, we can use it to find the length of the diagonal of a rectangle given the lengths of the sides. d2 = 10.22 + 13.62 d2 = 104.04 + 184.96 d2 = 289 d = 17 cm<br>
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Finding the lengths of diagonals Use Pythagoras’ Theorem to calculate the length d of the diagonal in a square of side length 7 cm. 7 cm Using Pythagoras’ Theorem d2 = 72 + 72 d2 = 49 + 49 d2 = 98 d = 9.90 cm (to 2 d.p.) d In a square and a rhombus, the diagonals bisect each other at right angles.<br>
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Finding the lengths of diagonals A rhombus has diagonals of length 6 cm and 8cm. Find the length of its sides Using Pythagoras’ Theorem x2 = 42 + 32 x2 = 16 + 9 x2 = 25 x = 5 cm 8 cm 6 cm The diagonals of the rhombus bisect at right angles. 4 cm 3 cm 4 cm x 3 cm Let each side of the rhombus have length x cm.<br>
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Finding the height of an isosceles triangle Use Pythagoras’ Theorem to calculate the height h of this isosceles triangle. 8 cm h2 + 42 = 5.82 h2 = 5.82 – 42 h2 = 33.64 – 16 h2 = 17.64 = 4.2 cm 5.8 cm h Using Pythagoras’ Theorem in half of the isosceles triangle, we have In an isosceles triangle and an equilateral triangle, the altitude bisects the base at right angles. isosceles triangle equilateral triangle 4 cm 4 cm<br>
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Finding the height of an equilateral triangle Use Pythagoras’ Theorem to calculate the height h of an equilateral triangle with side length 4 cm. h2 + 22 = 42 h2 = 42 – 22 h2 = 16 – 4 h2 = 12 h ≈ 3.46 cm (to 3sf) 4 cm Using Pythagoras’ Theorem in half of the equilateral triangle, we have 2 cm h exact answer<br>
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