Question

Is corner A of this piece of a wood square (90 degrees)? Explain... the corner piece has 13in diagonal edge and 12in vertical and a 5in horizontal...

Answer 1

I think what they want is to use Pythagorean Theorem to determine if it's 90°.
The theorem states that, if a triangle has a right angle, the hypotenuse, called "c", relates to the other sides a and b as follows:

`{c}^(2) = {a}^(2) + {b}^(2)`
the diagonal of the square is the hypotenuse c, so therefore c = 13 in.
we'll make a = 5, and b = 12

`{c}^(2) = {a}^(2) + {b}^(2) \\ \sqrt{ {c}^(2) } = \sqrt{( {a}^(2) + {b}^(2) ) } \\ c \: = \sqrt{( {a}^(2) + {b}^(2) ) } \\ 13= \sqrt{( {5}^(2) + {12}^(2) ) }`

`13= √(( 25 + 144 ) ) \\ 13= √(( 169 ) ) = 13`
So it's true! since 13 = 13, the corner is in fact a right angle!!