Question
right triangle with lengths of 15 and 3 what is the missing length rounded to the nearest tenth
Answers
Answered by
GPT-4o mini
To find the missing length of a right triangle when you have two sides, you can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the hypotenuse (the longest side), and \( a \) and \( b \) are the other two sides.
Assuming that the hypotenuse is the side of length 15 and one of the other sides is 3, we can denote:
- \( a = 3 \)
- \( c = 15 \)
We need to find \( b \):
\[ a^2 + b^2 = c^2 \]
Substituting the known values:
\[ 3^2 + b^2 = 15^2 \]
Calculating the squares:
\[ 9 + b^2 = 225 \]
Now, subtract 9 from both sides:
\[ b^2 = 225 - 9 \]
\[ b^2 = 216 \]
Now, take the square root of both sides to find \( b \):
\[ b = \sqrt{216} \]
To simplify \( \sqrt{216} \):
\[ \sqrt{216} = \sqrt{36 \times 6} = \sqrt{36} \times \sqrt{6} = 6\sqrt{6} \]
Now, calculate \( 6\sqrt{6} \) approximately:
Since \( \sqrt{6} \approx 2.449 \):
\[ 6\sqrt{6} \approx 6 \times 2.449 \approx 14.694 \]
Rounding this to the nearest tenth:
**The missing length is approximately 14.7.**
\[ a^2 + b^2 = c^2 \]
where \( c \) is the hypotenuse (the longest side), and \( a \) and \( b \) are the other two sides.
Assuming that the hypotenuse is the side of length 15 and one of the other sides is 3, we can denote:
- \( a = 3 \)
- \( c = 15 \)
We need to find \( b \):
\[ a^2 + b^2 = c^2 \]
Substituting the known values:
\[ 3^2 + b^2 = 15^2 \]
Calculating the squares:
\[ 9 + b^2 = 225 \]
Now, subtract 9 from both sides:
\[ b^2 = 225 - 9 \]
\[ b^2 = 216 \]
Now, take the square root of both sides to find \( b \):
\[ b = \sqrt{216} \]
To simplify \( \sqrt{216} \):
\[ \sqrt{216} = \sqrt{36 \times 6} = \sqrt{36} \times \sqrt{6} = 6\sqrt{6} \]
Now, calculate \( 6\sqrt{6} \) approximately:
Since \( \sqrt{6} \approx 2.449 \):
\[ 6\sqrt{6} \approx 6 \times 2.449 \approx 14.694 \]
Rounding this to the nearest tenth:
**The missing length is approximately 14.7.**