Question

The diagram shows a triangle ABC in which AB= 6 cm, BC=8 cm and ABC = 90°.

Calculate the length of AC.

The answer should be 12. please help with explanation and calculation!!!

Answer 1

AC =10 cm

Explanation:

triangle ABC is a right angled triangle

side opposite to angle B is hypotenuse

so hypotenuse=AC

here AB and BC are other two smaller sides of a triangle.

so according to pythagoras theorem sum of square of two smaller sides of a triangle must equal to the square of hypotenuse.

Let AB=a , BC=b and AC=c(hypotenuse)

`AB^(2)` +
`BC^(2)` =
`AC^(2)`

`6^(2)` +
`8^(2)` =
`AC^(2)`

36 + 64 =
`AC^(2)`

100=
`AC^(2)`

`\sqrt{100` =AC

10=AC