Using the Pythagorean theorem, find the length of a leg of a right triangle if the other leg is 8 feet long and the hypotenuse is 10 feet long.

Question

Question 20 options:

A)

36 ft.

B)

√ 41 ft.

C)

12.81 ft.

D)

6 ft.

Answer 1

To find the length of a leg of a right triangle using the Pythagorean theorem, we can use the formula:

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

where:

• \( c \) is the length of the hypotenuse,
• \( a \) and \( b \) are the lengths of the legs.

In this case, we know:

• One leg \( a = 8 \) feet,
• The hypotenuse \( c = 10 \) feet,
• We need to find the other leg \( b \).

Plugging the known values into the formula:

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

Calculating the squares:

\[ 64 + b^2 = 100 \]

Now, isolate \( b^2 \):

\[ b^2 = 100 - 64 \]

\[ b^2 = 36 \]

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

\[ b = \sqrt{36} \]

\[ b = 6 \text{ feet} \]

So the length of the other leg of the triangle is 6 feet.

Therefore, the correct answer is:

D) 6 ft.