Question
What is the length of the unknown leg of the right triangle?
6 ft
5 ft
(The figure is not drawn to scale.)
Question content area bottom
Part 1
The length of the unknown leg of the right triangle is
enter your response here ft.
(Round to one decimal place as needed.)
6 ft
5 ft
(The figure is not drawn to scale.)
Question content area bottom
Part 1
The length of the unknown leg of the right triangle is
enter your response here ft.
(Round to one decimal place as needed.)
Answers
GPT-4o mini
To find the length of the unknown leg of a right triangle, we can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where:
- \( c \) is the length of the hypotenuse,
- \( a \) and \( b \) are the lengths of the two legs.
In this case, you have provided the lengths of one leg (5 ft) and the hypotenuse (6 ft). We'll define the unknown leg as \( x \).
Using the Pythagorean theorem:
\[ 5^2 + x^2 = 6^2 \]
Calculating the squares gives:
\[ 25 + x^2 = 36 \]
Now, subtract 25 from both sides:
\[ x^2 = 36 - 25 \]
\[ x^2 = 11 \]
Now take the square root of both sides to find \( x \):
\[ x = \sqrt{11} \]
Calculating the square root:
\[ x \approx 3.3166 \]
Rounding to one decimal place:
\[ x \approx 3.3 \]
Therefore, the length of the unknown leg of the right triangle is approximately **3.3 ft**.
\[ a^2 + b^2 = c^2 \]
where:
- \( c \) is the length of the hypotenuse,
- \( a \) and \( b \) are the lengths of the two legs.
In this case, you have provided the lengths of one leg (5 ft) and the hypotenuse (6 ft). We'll define the unknown leg as \( x \).
Using the Pythagorean theorem:
\[ 5^2 + x^2 = 6^2 \]
Calculating the squares gives:
\[ 25 + x^2 = 36 \]
Now, subtract 25 from both sides:
\[ x^2 = 36 - 25 \]
\[ x^2 = 11 \]
Now take the square root of both sides to find \( x \):
\[ x = \sqrt{11} \]
Calculating the square root:
\[ x \approx 3.3166 \]
Rounding to one decimal place:
\[ x \approx 3.3 \]
Therefore, the length of the unknown leg of the right triangle is approximately **3.3 ft**.