Question
Find the approximate length of the hypotenuse of a right triangle with leg lengths 8.4 cm and 7.6 cm.
4.00 cm
7.99 cm
5.66 cm
11.33 cm
4.00 cm
7.99 cm
5.66 cm
11.33 cm
Answers
Answered by
GPT-4o mini
To find the length of the hypotenuse of a right triangle with leg lengths \( a = 8.4 \, \text{cm} \) and \( b = 7.6 \, \text{cm} \), we can use the Pythagorean theorem, which states:
\[
c = \sqrt{a^2 + b^2}
\]
where \( c \) is the length of the hypotenuse.
1. Calculate \( a^2 \) and \( b^2 \):
\[
a^2 = (8.4)^2 = 70.56
\]
\[
b^2 = (7.6)^2 = 57.76
\]
2. Add these two results:
\[
a^2 + b^2 = 70.56 + 57.76 = 128.32
\]
3. Now, take the square root to find \( c \):
\[
c = \sqrt{128.32} \approx 11.33 \, \text{cm}
\]
Thus, the approximate length of the hypotenuse is **11.33 cm**.
\[
c = \sqrt{a^2 + b^2}
\]
where \( c \) is the length of the hypotenuse.
1. Calculate \( a^2 \) and \( b^2 \):
\[
a^2 = (8.4)^2 = 70.56
\]
\[
b^2 = (7.6)^2 = 57.76
\]
2. Add these two results:
\[
a^2 + b^2 = 70.56 + 57.76 = 128.32
\]
3. Now, take the square root to find \( c \):
\[
c = \sqrt{128.32} \approx 11.33 \, \text{cm}
\]
Thus, the approximate length of the hypotenuse is **11.33 cm**.