# Right Triangle Find Hypotenuse

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 opposite) angle A, while side b is the side adjacent to angle A and opposed to angle B. (Source: Wikipedia)

## Example problems for finding right triangle hypotenuse

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

Hypotenuse (AC) = x

Find Hypotenuse value,

AB2 + BC2 = AC2

32 + 42 = x2

x2 = 25

x = 5

Hypotenuse value x = 5.

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

Hypotenuse (PR) = y

Find Hypotenuse value,

PQ2 + QR2 = PR2

122 + 162 = x2

x2 = 400

x = 20

Hypotenuse value x = 20

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

Hypotenuse (TS) = x

Find Hypotenuse value,

RT2 + SR2 = TS2

62 + 82 = x2

x2 =100

x = 10

Hypotenuse value x = 10.

The Hypotenuse value is 10.

## Practice problems for finding hypotenuse value

Right triangle hypotenuse problem 1:

Find the hypotenuse value of the given right triangle.

The hypotenuse value x = 25

Right triangle hypotenuse problem 2:

Find the hypotenuse value of the given right triangle.