A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90 degree angle). The side opposite the right
angle is called the hypotenuse (side *c* in the figure above). The sides adjacent to the right angle are called legs (or catheti, singular: cathetus). Side
*a* may be identified as the side adjacent to angle B and opposed to (or opposit*e*) *angle A*, while side *b* is the side *a*djacent to angle A and opposed to
angle B. (Source: Wikipedia)

**Right triangle hypotenuse problem 1:**

Find the hypotenuse value of the given right triangle.

**Solution:**

From the given right triangle ABC, we have to find out the hypotenuse value.

Using pythagoras theorem,

(opposite side)^{2} + (adjacent side)^{2} = (hypotenuse)^{2}

From the right triangle ABC,

Opposite side (AB) = 3

Adjacent side (BC) = 4

Hypotenuse (AC) = x

Find Hypotenuse value,

AB^{2} + BC^{2} = AC^{2}

3^{2} + 4^{2} = x^{2}

x^{2} = 25

x = 5

Hypotenuse value x = 5.

**Answer:**

The Hypotenuse value is 5.

**Right triangle hypotenuse problem 2:**

Find the hypotenuse value of the given right triangle.

**Solution:**

From the given right triangle PQR, we have to find out the hypotenuse value.

Using pythagoras theorem,

(opposite side)^{2} + (adjacent side)^{2} = (hypotenuse)^{2}

From the right trianglePQR,

Opposite side (PQ) = 3

Adjacent side (QR) = 4

Hypotenuse (PR) = y

Find Hypotenuse value,

PQ^{2} + QR^{2} = PR^{2}

12^{2} + 16^{2} = x^{2}

x^{2} = 400

x = 20

Hypotenuse value x = 20

**Answer:**

The Hypotenuse value is 20.

**Right triangle hypotenuse problem 3:**

Find the hypotenuse value of the given right triangle.

**Solution:**

From the given right triangle SRT, we have to find out the hypotenuse value.

Using pythagoras theorem,

(opposite side)^{2} + (adjacent side)^{2} = (hypotenuse)^{2}

From the right triangle ABC,

Opposite side (RT) = 3

Adjacent side (SR) = 4

Hypotenuse (TS) = x

Find Hypotenuse value,

RT^{2} + SR^{2} = TS^{2}

6^{2} + 8^{2} = x^{2}

x^{2} =100

x = 10

Hypotenuse value x = 10.

**Answer:**

The Hypotenuse value is 10.

**Right triangle hypotenuse problem 1:**

Find the hypotenuse value of the given right triangle.

**Answer:**

The hypotenuse value x = 25

**Right triangle hypotenuse problem 2:**

Find the hypotenuse value of the given right triangle.

**Answer:**

The hypotenuse value is 55