Question
Use Pythagorean theorem to find (a) if b=82 m and c= 99 m of the right angle triangle.
Answers
GPT-4o mini
In a right triangle, the Pythagorean theorem states that:
\[ c^2 = a^2 + b^2 \]
where:
- \( c \) is the length of the hypotenuse,
- \( a \) and \( b \) are the lengths of the other two sides.
In your case, you have \( b = 82 \, \text{m} \) and \( c = 99 \, \text{m} \). We need to find \( a \).
1. Start by substituting the values into the Pythagorean theorem:
\[
99^2 = a^2 + 82^2
\]
2. Calculate \( 99^2 \) and \( 82^2 \):
\[
99^2 = 9801
\]
\[
82^2 = 6724
\]
3. Substitute these values into the equation:
\[
9801 = a^2 + 6724
\]
4. Solve for \( a^2 \):
\[
a^2 = 9801 - 6724
\]
\[
a^2 = 3077
\]
5. Finally, take the square root to find \( a \):
\[
a = \sqrt{3077} \approx 55.5 \, \text{m}
\]
Thus, the length of side \( a \) is approximately \( 55.5 \, \text{m} \).
\[ c^2 = a^2 + b^2 \]
where:
- \( c \) is the length of the hypotenuse,
- \( a \) and \( b \) are the lengths of the other two sides.
In your case, you have \( b = 82 \, \text{m} \) and \( c = 99 \, \text{m} \). We need to find \( a \).
1. Start by substituting the values into the Pythagorean theorem:
\[
99^2 = a^2 + 82^2
\]
2. Calculate \( 99^2 \) and \( 82^2 \):
\[
99^2 = 9801
\]
\[
82^2 = 6724
\]
3. Substitute these values into the equation:
\[
9801 = a^2 + 6724
\]
4. Solve for \( a^2 \):
\[
a^2 = 9801 - 6724
\]
\[
a^2 = 3077
\]
5. Finally, take the square root to find \( a \):
\[
a = \sqrt{3077} \approx 55.5 \, \text{m}
\]
Thus, the length of side \( a \) is approximately \( 55.5 \, \text{m} \).