Question
What is the length of side a? Round to the nearest tenth of an inch. Enter your answer in the box.
A right triangle with legs 7 inches and A inches and hypotenuse 16 inches.
About
in.
A right triangle with legs 7 inches and A inches and hypotenuse 16 inches.
About
in.
Answers
GPT-4o mini
To find the length of side \( a \) (one of the legs of the right triangle), we can use the Pythagorean theorem, which states:
\[
a^2 + b^2 = c^2
\]
where \( a \) and \( b \) are the lengths of the legs and \( c \) is the length of the hypotenuse.
Given:
- One leg \( b = 7 \) inches
- Hypotenuse \( c = 16 \) inches
We can plug in these values into the equation:
\[
a^2 + 7^2 = 16^2
\]
Calculating the squares:
\[
a^2 + 49 = 256
\]
Now, we can isolate \( a^2 \):
\[
a^2 = 256 - 49
\]
\[
a^2 = 207
\]
Next, we take the square root to find \( a \):
\[
a = \sqrt{207}
\]
\[
a \approx 14.4 \text{ inches} \quad (\text{rounded to the nearest tenth})
\]
Thus, the length of side \( a \) is approximately **14.4 inches**.
\[
a^2 + b^2 = c^2
\]
where \( a \) and \( b \) are the lengths of the legs and \( c \) is the length of the hypotenuse.
Given:
- One leg \( b = 7 \) inches
- Hypotenuse \( c = 16 \) inches
We can plug in these values into the equation:
\[
a^2 + 7^2 = 16^2
\]
Calculating the squares:
\[
a^2 + 49 = 256
\]
Now, we can isolate \( a^2 \):
\[
a^2 = 256 - 49
\]
\[
a^2 = 207
\]
Next, we take the square root to find \( a \):
\[
a = \sqrt{207}
\]
\[
a \approx 14.4 \text{ inches} \quad (\text{rounded to the nearest tenth})
\]
Thus, the length of side \( a \) is approximately **14.4 inches**.