Question
what is the length of the missing leg if necessary round to the nearest tenth 15cm 12 cm
Answers
GPT-4o mini
To find the length of the missing leg in a right triangle where the legs are 15 cm and 12 cm, you can use the Pythagorean theorem. The theorem states that:
\[ c^2 = a^2 + b^2 \]
where \( c \) is the hypotenuse, and \( a \) and \( b \) are the legs of the triangle.
However, since you want the missing leg, let's assume you have one leg (15 cm) and the hypotenuse (12 cm). But in a right triangle, the hypotenuse is always the longest side, which means we need to assume that the missing leg is the one we need to calculate, and given that the longest leg is 15 cm, we'll calculate using that value.
Let's denote the legs as:
- \( a = 12 \) cm (one leg)
- \( b \) = unknown leg
- \( c = 15 \) cm (hypotenuse)
Using the Pythagorean theorem:
\[ 15^2 = 12^2 + b^2 \]
Calculating the squares:
\[ 225 = 144 + b^2 \]
Now, subtract 144 from both sides:
\[ b^2 = 225 - 144 \]
\[ b^2 = 81 \]
Taking the square root of both sides gives us:
\[ b = \sqrt{81} \]
\[ b = 9 \, \text{cm} \]
Thus, the length of the missing leg is **9.0 cm** (already rounded to the nearest tenth).
\[ c^2 = a^2 + b^2 \]
where \( c \) is the hypotenuse, and \( a \) and \( b \) are the legs of the triangle.
However, since you want the missing leg, let's assume you have one leg (15 cm) and the hypotenuse (12 cm). But in a right triangle, the hypotenuse is always the longest side, which means we need to assume that the missing leg is the one we need to calculate, and given that the longest leg is 15 cm, we'll calculate using that value.
Let's denote the legs as:
- \( a = 12 \) cm (one leg)
- \( b \) = unknown leg
- \( c = 15 \) cm (hypotenuse)
Using the Pythagorean theorem:
\[ 15^2 = 12^2 + b^2 \]
Calculating the squares:
\[ 225 = 144 + b^2 \]
Now, subtract 144 from both sides:
\[ b^2 = 225 - 144 \]
\[ b^2 = 81 \]
Taking the square root of both sides gives us:
\[ b = \sqrt{81} \]
\[ b = 9 \, \text{cm} \]
Thus, the length of the missing leg is **9.0 cm** (already rounded to the nearest tenth).