In triangle ABC, AB=5 cm, BC=12 cm and angle ABC=90 degree, calculate the length of AC.

triangle ABC have angle ABC 90 degree. therefore the triangle ABC is right angled triangle.

Therefore, In triangle ABC,
by phyathagoras theorem,
AC ¡Á AC =AB¡ÁAB BC ¡ÁBC
AC ¡Á AC = 5¡Á5 12¡Á12
= 25 144
=169
Therefore, AC =13

ac=13

To calculate the length of AC in triangle ABC, we can use the Pythagorean theorem since angle ABC is a right angle.

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Mathematically, it can be expressed as:

c^2 = a^2 + b^2

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

In this case, AB is the side adjacent to angle C and BC is the side opposite angle C. So, we can use the theorem to find the length of AC.

Substituting the given values into the equation:

AC^2 = AB^2 + BC^2
AC^2 = 5^2 + 12^2
AC^2 = 25 + 144
AC^2 = 169

To find the length of AC, we need to find the square root of both sides:

AC = √169
AC = 13 cm

Therefore, the length of AC in triangle ABC is 13 cm.

To find the length AC in triangle ABC, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In triangle ABC, AB is one of the legs and BC is the other leg. AC is the hypotenuse.

So, we can use the formula: AC^2 = AB^2 + BC^2

Plugging in the given values:
AC^2 = 5^2 + 12^2

Simplifying the equation:
AC^2 = 25 + 144
AC^2 = 169

Now, to find the length AC, we take the square root of both sides:
√(AC^2) = √169

AC = 13 cm

Therefore, the length of AC in triangle ABC is 13 cm.