Question

Find the length of the third side. If necessary round to the nearest tenth

Answer 1

The side lengths of a right-angle triangle can be calculated using the Pythagorean Theorem. Which states that the square of the hypotenuse is equal to the sum of squares of the other sides in the triangle.

`a^2+b^2=c^2`

• the hypotenuse is always the longest side of a triangle and is always the opposite side length to the right angle

rearranging the equation can help calculate the third side:

`c^2-a^2=b^2`

`(5)^2-(4)^2=b^2`

`25-16=b^2`

`9=b^2`

`√(9)=√(b^2)`

`{ {{b_1=+3} \atop {b_2=-3}} \right.`

note: a length can never be negative so never take into account a negative answer

b = 3