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CHERLYNnotCHERRY

Answer:

The length of BC is √105 cm or 10.2 cm.

Step-by-step explanation:

You have to apply Pythagoras Theorem, c² = a² + b² where c represents hypotenuse, a and b are the sides :

[tex] {c}^{2} = { a}^{2} + {b}^{2} [/tex]

[tex]let \:a =BC \:, \: b = 8 \: , \: c = 13[/tex]

[tex] {13}^{2} = {BC}^{2} + {8}^{2} [/tex]

[tex]169 = {BC}^{2} + 64[/tex]

[tex] {BC}^{2} = 169 - 64[/tex]

[tex] {BC}^{2} = 105[/tex]

[tex]BC = \sqrt{105} [/tex]

[tex]BC = 10.2 \: cm \: (3s.f)[/tex]

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Answer:

[tex] \boxed{\sf Length \ of \ BC = \sqrt{105} \ cm} [/tex]

Given:

AB = 13 cm

AC = 8 cm

To Find:

Length of BC

Step-by-step explanation:

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.

[tex] \therefore \\ \sf {AC}^{2} + {BC}^{2} = {AB}^{2} \\ \sf \implies {8}^{2} + {BC}^{2} = {13}^{2} \\ \\ \sf {8}^{2} = 64 : \\ \sf \implies 64 + {BC}^{2} = {13}^{2} \\ \\ \sf {13}^{2} = 169 : \\ \sf \implies 64 + {BC}^{2} = 169 \\ \\ \sf Substract \: 64 \: from \: both \: sides : \\ \sf \implies (64 - 64) + {BC}^{2} = 169 - 64 \\ \\ \sf 64 - 64 = 0 : \\ \sf \implies {BC}^{2} = 169 - 64 \\ \\ \sf 169 - 64 = 105 : \\ \sf \implies {BC}^{2} = 105 \\ \\ \sf \implies BC = \sqrt{ 105 } \ cm [/tex]

So,

Length of BC = [tex] \sqrt{105} [/tex] cm

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