**Introduction:**

A **right triangle** (or **right-angled triangle**, formerly called a **rectangle triangle**) has one of its interior angles measuring 90° (a right angle).
The side opposite to the right angle is the hypotenuse; it is the longest side of the right triangle. The other two sides are called the *legs* of the triangle.

Right triangles obey the Pythagorean Theorem: the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse: *a*^{2} +
*b*^{2} = *c*^{2}, where *a* and *b* are the lengths of the legs and *c* is the length of the hypotenuse. Special right triangles are right
triangles with additional properties that make calculations involving them easier. The most famous is the 3-4-5 right triangle, where *3*^{2} + *4*^{2} =
*5*^{2}. In this situation, 3, 4, and 5 are a Pythagorean Triple.(Source from Wikipedia).

Using the calculator, we can find the value of hypotenuse when the two sides are known.

Hypotenuse triangle calculator

**Example problem 1:**

Find the hypotenuse of the triangle when the two sides are a=8cm and b=6cm.

**Given:**

Right angle triangle

a=8cm and b=6cm

**Solution:**

If we substitute the side values a and b in the calculator, then we get the hypotenuse value.

Using Pythagorean theorem, we have to find the hypotenuse.

: *a*^{2} + *b*^{2} = *c*^{2}

*8*^{2} + *6*^{2} = *c*^{2}

64+36= *c*^{2}

100= *c*^{2}

C=10cm

So, the hypotenuse of the triangle is c=10cm.

**Example problem 2:**

Find the hypotenuse of the triangle when the two sides are a=1.5cm and b=2cm.

**Given:**

Right angle triangle

a=1.5cm and b=2cm

**Solution:**

If we substitute the side values a and b in the calculator, then we get the hypotenuse value.

Using Pythagorean theorem, we have to find the hypotenuse.

: *a*^{2} + *b*^{2} = *c*^{2}

*(1.5)*^{2} + *2*^{2} = *c*^{2}

2.25+4= *c*^{2}

6.25= *c*^{2}

C=2.5cm

So, the hypotenuse of the triangle is c=2.5cm.

**Example problem 3:**

Find the hypotenuse of the triangle when the two sides are a=7cm and b=8cm.

**Given:**

Right angle triangle

a=7cm and b=8cm

**Solution:**

If we substitute the side values a and b in the calculator, then we get the hypotenuse value.

Using Pythagorean theorem, we have to find the hypotenuse.

: *a*^{2} + *b*^{2} = *c*^{2}

*(7)*^{2} + *8*^{2} = *c*^{2}

49+64= *c*^{2}

113= *c*^{2}

C=10.63cm

So, the hypotenuse of the triangle is c=10.63cm.