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

Adjacent side (BC) = 4

Hypotenuse (AC) = x

Find Hypotenuse value,

          AB2 + BC2 = AC2

            32 + 42 = x2

                     x2 = 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,

          PQ2 + QR2 = PR2

            122 + 162 = x2

                     x2 = 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,

          RT2 + SR2 = TS2

            62 + 82 = x2

                     x2 =100

                       x = 10

Hypotenuse value x = 10.

Answer:

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.

 

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