Question
right angle triangle with lengths of 60 and 80
Answers
Answered by
GPT-4o mini
In a right triangle, the lengths of the two legs are given as 60 and 80. To find the length of the hypotenuse, you can use the Pythagorean theorem, which states:
\[
c^2 = a^2 + b^2
\]
where:
- \( c \) is the length of the hypotenuse,
- \( a \) and \( b \) are the lengths of the legs.
In this case, \( a = 60 \) and \( b = 80 \):
\[
c^2 = 60^2 + 80^2
\]
Calculating \( 60^2 \) and \( 80^2 \):
\[
60^2 = 3600
\]
\[
80^2 = 6400
\]
Adding these together:
\[
c^2 = 3600 + 6400 = 10000
\]
Now, take the square root to find \( c \):
\[
c = \sqrt{10000} = 100
\]
Thus, the lengths of the sides of the right triangle are 60, 80, and 100.
\[
c^2 = a^2 + b^2
\]
where:
- \( c \) is the length of the hypotenuse,
- \( a \) and \( b \) are the lengths of the legs.
In this case, \( a = 60 \) and \( b = 80 \):
\[
c^2 = 60^2 + 80^2
\]
Calculating \( 60^2 \) and \( 80^2 \):
\[
60^2 = 3600
\]
\[
80^2 = 6400
\]
Adding these together:
\[
c^2 = 3600 + 6400 = 10000
\]
Now, take the square root to find \( c \):
\[
c = \sqrt{10000} = 100
\]
Thus, the lengths of the sides of the right triangle are 60, 80, and 100.