Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Get accurate and detailed answers to your questions from a dedicated community of experts on our Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
To find the length of the altitude of an equilateral triangle with side length 8 units, we can use the geometric properties of equilateral triangles.
1. Understanding the properties of the equilateral triangle:
- In an equilateral triangle, all sides are equal, and all angles are 60 degrees.
- The altitude of an equilateral triangle splits the triangle into two 30-60-90 right triangles.
2. Relationship in a 30-60-90 triangle:
- In a 30-60-90 triangle, the ratios of the sides are:
- The side opposite the 30° angle is the shortest side.
- The side opposite the 60° angle (which is the altitude in our case) is equal to the shortest side times [tex]\(\sqrt{3}\)[/tex].
- The hypotenuse (which in our case is the side of the equilateral triangle) is twice the shortest side.
3. Determine the lengths of sides in the right triangle:
- The hypotenuse is the side of the equilateral triangle, which is 8 units.
- The shortest side (half of the equilateral triangle's side) is [tex]\( \frac{8}{2} = 4 \)[/tex] units.
4. Calculate the altitude:
- Using the property of the 30-60-90 triangle, the altitude is the shortest side times [tex]\(\sqrt{3}\)[/tex].
- Therefore, the altitude is [tex]\( 4 \times \sqrt{3} \)[/tex].
Using the above reasoning, the altitude of this equilateral triangle is:
[tex]\[ 4 \sqrt{3} \text{ units} \][/tex]
So, the correct answer is [tex]\( 4 \sqrt{3} \)[/tex] units.
1. Understanding the properties of the equilateral triangle:
- In an equilateral triangle, all sides are equal, and all angles are 60 degrees.
- The altitude of an equilateral triangle splits the triangle into two 30-60-90 right triangles.
2. Relationship in a 30-60-90 triangle:
- In a 30-60-90 triangle, the ratios of the sides are:
- The side opposite the 30° angle is the shortest side.
- The side opposite the 60° angle (which is the altitude in our case) is equal to the shortest side times [tex]\(\sqrt{3}\)[/tex].
- The hypotenuse (which in our case is the side of the equilateral triangle) is twice the shortest side.
3. Determine the lengths of sides in the right triangle:
- The hypotenuse is the side of the equilateral triangle, which is 8 units.
- The shortest side (half of the equilateral triangle's side) is [tex]\( \frac{8}{2} = 4 \)[/tex] units.
4. Calculate the altitude:
- Using the property of the 30-60-90 triangle, the altitude is the shortest side times [tex]\(\sqrt{3}\)[/tex].
- Therefore, the altitude is [tex]\( 4 \times \sqrt{3} \)[/tex].
Using the above reasoning, the altitude of this equilateral triangle is:
[tex]\[ 4 \sqrt{3} \text{ units} \][/tex]
So, the correct answer is [tex]\( 4 \sqrt{3} \)[/tex] units.
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.