Question
What is the length of the missing leg? If necessary, round to the nearest tenth. The slope is 9.9 and the height is 7.2)
Round decimals to the nearest tenth.
Round decimals to the nearest tenth.
Answers
GPT-4o mini
To find the length of the missing leg in a right triangle, given the slope (the hypotenuse) and the height (one leg), we can use the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
Where:
- \( c \) is the hypotenuse (slope),
- \( a \) is the height (one leg),
- \( b \) is the missing leg.
In this case:
- \( c = 9.9 \)
- \( a = 7.2 \)
We need to find \( b \):
\[
b^2 = c^2 - a^2
\]
Plugging in the values:
\[
b^2 = (9.9)^2 - (7.2)^2
\]
Calculating the squares:
\[
(9.9)^2 = 98.01
\]
\[
(7.2)^2 = 51.84
\]
Now substitute these values back into the equation:
\[
b^2 = 98.01 - 51.84
\]
\[
b^2 = 46.17
\]
Now take the square root to solve for \( b \):
\[
b = \sqrt{46.17} \approx 6.8
\]
Therefore, the length of the missing leg is approximately **6.8** (rounded to the nearest tenth).
\[
a^2 + b^2 = c^2
\]
Where:
- \( c \) is the hypotenuse (slope),
- \( a \) is the height (one leg),
- \( b \) is the missing leg.
In this case:
- \( c = 9.9 \)
- \( a = 7.2 \)
We need to find \( b \):
\[
b^2 = c^2 - a^2
\]
Plugging in the values:
\[
b^2 = (9.9)^2 - (7.2)^2
\]
Calculating the squares:
\[
(9.9)^2 = 98.01
\]
\[
(7.2)^2 = 51.84
\]
Now substitute these values back into the equation:
\[
b^2 = 98.01 - 51.84
\]
\[
b^2 = 46.17
\]
Now take the square root to solve for \( b \):
\[
b = \sqrt{46.17} \approx 6.8
\]
Therefore, the length of the missing leg is approximately **6.8** (rounded to the nearest tenth).