At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
To solve for the length of one leg in a 45°-45°-90° triangle where the hypotenuse measures 4 cm, we can utilize the special properties of this type of triangle.
A 45°-45°-90° triangle, also known as an isosceles right triangle, has sides that follow a specific ratio:
- The legs are of equal length.
- The hypotenuse is [tex]\( \sqrt{2} \)[/tex] times the length of each leg.
Given the hypotenuse ([tex]\(c\)[/tex]) is 4 cm, we can denote the length of each leg as [tex]\(a\)[/tex]. According to the relationship in a 45°-45°-90° triangle, the hypotenuse is [tex]\( \sqrt{2} \)[/tex] times the leg:
[tex]\[ c = a \sqrt{2} \][/tex]
Substitute the given hypotenuse length into the equation:
[tex]\[ 4 = a \sqrt{2} \][/tex]
To find the length of the leg [tex]\(a\)[/tex], solve for [tex]\(a\)[/tex]:
[tex]\[ a = \frac{4}{\sqrt{2}} \][/tex]
Rationalize the denominator by multiplying the numerator and the denominator by [tex]\(\sqrt{2}\)[/tex]:
[tex]\[ a = \frac{4 \cdot \sqrt{2}}{\sqrt{2} \cdot \sqrt{2}} \][/tex]
[tex]\[ a = \frac{4 \sqrt{2}}{2} \][/tex]
[tex]\[ a = 2 \sqrt{2} \][/tex]
Thus, the length of one leg of the triangle is:
[tex]\[ 2 \sqrt{2} \text{ cm} \][/tex]
So the correct answer is:
[tex]\[ \boxed{2 \sqrt{2} \text{ cm}} \][/tex]
A 45°-45°-90° triangle, also known as an isosceles right triangle, has sides that follow a specific ratio:
- The legs are of equal length.
- The hypotenuse is [tex]\( \sqrt{2} \)[/tex] times the length of each leg.
Given the hypotenuse ([tex]\(c\)[/tex]) is 4 cm, we can denote the length of each leg as [tex]\(a\)[/tex]. According to the relationship in a 45°-45°-90° triangle, the hypotenuse is [tex]\( \sqrt{2} \)[/tex] times the leg:
[tex]\[ c = a \sqrt{2} \][/tex]
Substitute the given hypotenuse length into the equation:
[tex]\[ 4 = a \sqrt{2} \][/tex]
To find the length of the leg [tex]\(a\)[/tex], solve for [tex]\(a\)[/tex]:
[tex]\[ a = \frac{4}{\sqrt{2}} \][/tex]
Rationalize the denominator by multiplying the numerator and the denominator by [tex]\(\sqrt{2}\)[/tex]:
[tex]\[ a = \frac{4 \cdot \sqrt{2}}{\sqrt{2} \cdot \sqrt{2}} \][/tex]
[tex]\[ a = \frac{4 \sqrt{2}}{2} \][/tex]
[tex]\[ a = 2 \sqrt{2} \][/tex]
Thus, the length of one leg of the triangle is:
[tex]\[ 2 \sqrt{2} \text{ cm} \][/tex]
So the correct answer is:
[tex]\[ \boxed{2 \sqrt{2} \text{ cm}} \][/tex]
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.