Question

what is the length of the missing leg if necessary round to the nearest tenth 7cm and 3cm and b at the bottem is missing

Answer 1

To find the length of the missing leg in a right triangle when given the lengths of the two other legs, you can use the Pythagorean theorem. The theorem 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.

In your case, it seems you're looking for the length of the missing leg \(b\), and you have one leg as 7 cm and the other as 3 cm.

Since we don’t know whether the 7 cm or the 3 cm is the hypotenuse, let's consider both scenarios:

1. **If 7 cm is the hypotenuse:**
\[
7^2 = 3^2 + b^2
\]
\[
49 = 9 + b^2
\]
\[
b^2 = 49 - 9
\]
\[
b^2 = 40
\]
\[
b = \sqrt{40} \approx 6.3 \text{ cm}
\]

2. **If 3 cm is the hypotenuse (which is not possible in this case as 3 cm < 7 cm):**
\[
3^2 = 7^2 + b^2
\]
\[
9 = 49 + b^2 \quad (not possible)
\]

Since the 3 cm cannot be the hypotenuse, the valid calculation shows that if 7 cm is the hypotenuse, the missing leg \(b\) is approximately **6.3 cm** when rounded to the nearest tenth.