Question

10 cm 8 cm b
What is the length of the missing leg? If necessary, round to the nearest tenth.
b=
centimeters

Answer 1

find b

Answer 2

To find the length of the missing leg \( b \) in a right triangle where the lengths of the other two legs are 10 cm and 8 cm, you can use the Pythagorean theorem:

\[
a^2 + b^2 = c^2
\]

However, since you haven't specified which leg is missing, I will assume you're looking for \( b \) where \( 10 \) cm is one leg and \( 8 \) cm is the other leg. We will find \( c \), the hypotenuse.

Using the Pythagorean theorem:

\[
10^2 + 8^2 = c^2
\]

Calculating:

\[
100 + 64 = c^2
\]

\[
164 = c^2
\]

Now take the square root of both sides to find \( c \):

\[
c = \sqrt{164} \approx 12.8 \text{ cm}
\]

If instead you meant to find \( b \) as a missing leg, in the case where you have a hypotenuse and one leg, please clarify and I can help with that scenario too!

Answer 3

To find the length of the missing leg \( b \) in a right triangle where one leg is 10 cm and the hypotenuse \( c \) is 8 cm, we will assume that you meant that the hypotenuse \( c \) is longer than the legs. However, in a right triangle, the hypotenuse must always be the longest side.

Let's clarify: Are you sure that the hypotenuse is 8 cm? If so, we cannot have a leg longer than the hypotenuse.

If we are meant to find the missing leg with one leg \( a = 8 \) cm and the hypotenuse \( c = 10 \) cm, then we can use the Pythagorean theorem:

\[
a^2 + b^2 = c^2
\]

Substituting in the values:

\[
8^2 + b^2 = 10^2
\]

Calculating:

\[
64 + b^2 = 100
\]

Now, subtract 64 from both sides:

\[
b^2 = 100 - 64
\]

\[
b^2 = 36
\]

Now, take the square root of both sides to find \( b \):

\[
b = \sqrt{36} = 6 \text{ cm}
\]

So the length of the missing leg \( b \) is **6 centimeters**.