Question
What is the length of the missing leg? If necessary, round to the nearest tenth. b=6.4 c=7.7 a=?
Answers
GPT-4o mini
To find the length of the missing leg \( a \) in a right triangle, we can use the Pythagorean theorem, which states:
\[
a^2 + b^2 = c^2
\]
where:
- \( a \) is the length of one leg,
- \( b \) is the length of the other leg,
- \( c \) is the length of the hypotenuse.
Given:
- \( b = 6.4 \)
- \( c = 7.7 \)
We need to solve for \( a \):
1. Substitute the known values into the Pythagorean theorem:
\[
a^2 + (6.4)^2 = (7.7)^2
\]
2. Calculate \( (6.4)^2 \) and \( (7.7)^2 \):
\[
(6.4)^2 = 40.96
\]
\[
(7.7)^2 = 59.29
\]
3. Now, substitute those values into the equation:
\[
a^2 + 40.96 = 59.29
\]
4. Solve for \( a^2 \):
\[
a^2 = 59.29 - 40.96
\]
\[
a^2 = 18.33
\]
5. Take the square root of both sides to find \( a \):
\[
a = \sqrt{18.33} \approx 4.3
\]
Thus, the length of the missing leg \( a \) is approximately **4.3** (rounded to the nearest tenth).
\[
a^2 + b^2 = c^2
\]
where:
- \( a \) is the length of one leg,
- \( b \) is the length of the other leg,
- \( c \) is the length of the hypotenuse.
Given:
- \( b = 6.4 \)
- \( c = 7.7 \)
We need to solve for \( a \):
1. Substitute the known values into the Pythagorean theorem:
\[
a^2 + (6.4)^2 = (7.7)^2
\]
2. Calculate \( (6.4)^2 \) and \( (7.7)^2 \):
\[
(6.4)^2 = 40.96
\]
\[
(7.7)^2 = 59.29
\]
3. Now, substitute those values into the equation:
\[
a^2 + 40.96 = 59.29
\]
4. Solve for \( a^2 \):
\[
a^2 = 59.29 - 40.96
\]
\[
a^2 = 18.33
\]
5. Take the square root of both sides to find \( a \):
\[
a = \sqrt{18.33} \approx 4.3
\]
Thus, the length of the missing leg \( a \) is approximately **4.3** (rounded to the nearest tenth).