Let's solve the problem of finding the length of the other leg of a right triangle where one leg is 10 units and the hypotenuse is 12 units.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two legs. Mathematically, this can be written as:
[tex]\[ \text{hypotenuse}^2 = \text{leg}_a^2 + \text{leg}_b^2 \][/tex]
We are given:
- Leg [tex]\( \text{leg}_a = 10 \)[/tex] units
- Hypotenuse [tex]\( \text{hypotenuse} = 12 \)[/tex] units
We need to find [tex]\( \text{leg}_b \)[/tex], the length of the other leg.
1. Calculate the square of [tex]\( \text{leg}_a \)[/tex]:
[tex]\[ \text{leg}_a^2 = 10^2 = 100 \][/tex]
2. Calculate the square of the hypotenuse:
[tex]\[ \text{hypotenuse}^2 = 12^2 = 144 \][/tex]
3. Use the Pythagorean theorem to find the square of the other leg [tex]\( \text{leg}_b \)[/tex]:
[tex]\[ \text{leg}_b^2 = \text{hypotenuse}^2 - \text{leg}_a^2 = 144 - 100 = 44 \][/tex]
4. Find the length of [tex]\( \text{leg}_b \)[/tex] by taking the square root of [tex]\( \text{leg}_b^2 \)[/tex]:
[tex]\[ \text{leg}_b = \sqrt{44} \approx 6.6332495807108 \][/tex]
Therefore, the length of the other leg is approximately [tex]\( 6.63 \)[/tex] units.
Looking at the given answer choices:
A. about 7 units
B. about 15 units
C. about 25 units
D. about 122 units
E. about 224 units
The closest answer to [tex]\( 6.63 \)[/tex] units is:
A. about 7 units
So, the correct answer is:
A. about 7 units
