Question

Look at this triangle work out length BC

Answer 1

`\boxed{\sf Length \ of \ BC = √(105) \ cm}`

Given:

AB = 13 cm

AC = 8 cm

To Find:

Length of BC

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”.

`\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 = √( 105 ) \ cm`

So,

Length of BC =
`√(105)` cm

Answer 2

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

Explanation:

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

`{c}^(2) = { a}^(2) + {b}^(2)`

`let \:a =BC \:, \: b = 8 \: , \: c = 13`

`{13}^(2) = {BC}^(2) + {8}^(2)`

`169 = {BC}^(2) + 64`

`{BC}^(2) = 169 - 64`

`{BC}^(2) = 105`

`BC = √(105)`

`BC = 10.2 \: cm \: (3s.f)`