Question
4 ft hight 5 ft slope
What is the length of the missing leg? If necessary, round to the nearest tenth.
a = _ centimeters
What is the length of the missing leg? If necessary, round to the nearest tenth.
a = _ centimeters
Answers
GPT-4o mini
To find the length of the missing leg of a right triangle when you know the height (one leg) and the slope (the hypotenuse), you can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where:
- \( a \) is one leg of the triangle,
- \( b \) is the other leg,
- \( c \) is the hypotenuse.
In this case:
- \( a = 4 \) ft (the height),
- \( c = 5 \) ft (the slope).
We want to find \( b \) (the missing leg). Rearranging the Pythagorean theorem gives us:
\[ b^2 = c^2 - a^2 \]
Now substitute the known values:
\[ b^2 = 5^2 - 4^2 \]
\[ b^2 = 25 - 16 \]
\[ b^2 = 9 \]
Now take the square root of both sides to find \( b \):
\[ b = \sqrt{9} = 3 \text{ ft} \]
Now to convert this length to centimeters, recall that 1 foot is equal to 30.48 centimeters. Thus:
\[ 3 \text{ ft} \times 30.48 \text{ cm/ft} = 91.44 \text{ cm} \]
So, the length of the missing leg is:
**a = 91.4 centimeters (rounded to the nearest tenth).**
\[ a^2 + b^2 = c^2 \]
where:
- \( a \) is one leg of the triangle,
- \( b \) is the other leg,
- \( c \) is the hypotenuse.
In this case:
- \( a = 4 \) ft (the height),
- \( c = 5 \) ft (the slope).
We want to find \( b \) (the missing leg). Rearranging the Pythagorean theorem gives us:
\[ b^2 = c^2 - a^2 \]
Now substitute the known values:
\[ b^2 = 5^2 - 4^2 \]
\[ b^2 = 25 - 16 \]
\[ b^2 = 9 \]
Now take the square root of both sides to find \( b \):
\[ b = \sqrt{9} = 3 \text{ ft} \]
Now to convert this length to centimeters, recall that 1 foot is equal to 30.48 centimeters. Thus:
\[ 3 \text{ ft} \times 30.48 \text{ cm/ft} = 91.44 \text{ cm} \]
So, the length of the missing leg is:
**a = 91.4 centimeters (rounded to the nearest tenth).**