Question
Asked By SilentSkies45 at
Answered By Expert
Scott
Expert ยท 5.4k answers ยท 5k people helped
To find the height of an equilateral triangle, we can use the properties of 30-60-90 triangles. In an equilateral triangle, the height splits the triangle into two 30-60-90 triangles.
Solution By Steps
Step 1: Identify the sides of a 30-60-90 triangle
In a 30-60-90 triangle, the sides are in the ratio of 1:โ3:2. The shortest side is opposite the 30-degree angle, the middle side is opposite the 60-degree angle, and the longest side is opposite the 90-degree angle (the hypotenuse).
Step 2: Apply the ratio to the equilateral triangle
In an equilateral triangle, each side is equal. If we assume the side length of the equilateral triangle is
s, then the hypotenuse of the 30-60-90 triangle formed by the height is also
s. The height
x corresponds to the side opposite the 60-degree angle in the 30-60-90 triangle.
Step 3: Calculate the height
Using the ratio 1:โ3:2, if the hypotenuse (which is also a side of the equilateral triangle) is
s, then the height
x is
\frac{s\sqrt{3}}{2}.
Final Answer
The height
x of the equilateral triangle is
\frac{s\sqrt{3}}{2}. Without a specific value for
s, we cannot determine a numerical answer from the given options.
๐งโ๐ซ More Questions
๐ Interested in exploring further?
Chrome Extension
1. Search answers from our 90+ million questions database.
2. Get instantly AI Solutions powered by most advanced models like GPT-4, Bard, Math GPT, etc.
3. Enjoy one-stop access to millions of textbook solutions.
4. Chat with 50+ AI study mates to get personalized course studies.
5. Ask your questions simply with texts or screenshots everywhere.