In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 7.7 centimeters and b = 2.8 centimeters, what is c? If necessary, round to the nearest tenth. c = _____ centimeters

To find the length of the hypotenuse ( c ) in a right triangle when the lengths of the legs ( a ) and ( b ) are given, we can use the Pythagorean theorem:

[

c^2 = a^2 + b^2

]

Given:

– ( a = 7.7 ) cm

– ( b = 2.8 ) cm

First, we will calculate ( a^2 ) and ( b^2 ):

1. ( a^2 = 7.7^2 = 59.29 )
2. ( b^2 = 2.8^2 = 7.84 )

Next, we add these values:

[

c^2 = 59.29 + 7.84 = 67.13

]

Now, we take the square root of both sides to find ( c ):

[

c = sqrt{67.13} approx 8.2 , text{cm} quad (text{rounded to the nearest tenth})

]

Thus, the length of the hypotenuse ( c ) is approximately 8.2 centimeters.

To find the length of the hypotenuse ( c ) in a right triangle when you know the lengths of the legs ( a ) and ( b ), you can use the Pythagorean theorem, which is:

[

c^2 = a^2 + b^2

]

Given:

– ( a = 7.7 ) cm

– ( b = 2.8 ) cm

1. Calculate ( a^2 ):

[

a^2 = (7.7)^2 = 59.29

]

2. Calculate ( b^2 ):

[

b^2 = (2.8)^2 = 7.84

]

3. Add ( a^2 ) and ( b^2 ):

[

a^2 + b^2 = 59.29 + 7.84 = 67.13

]

4. Now take the square root to find ( c ):

[

c = sqrt{67.13} approx 8.2 text{ cm}

]

So, the length of the hypotenuse ( c ) is approximately 8.2 centimeters.