To find the height of an equilateral triangle with side lengths of 7 inches, you can use the formula specifically for the height of an equilateral triangle, which is derived from the Pythagorean theorem. The formula is:
[tex]\[ h = \frac{a \sqrt{3}}{2} \][/tex]
where [tex]\(a\)[/tex] is the length of a side of the triangle.
Let's walk through the steps to find the height:
1. Identify the side length: The side length [tex]\(a\)[/tex] of the equilateral triangle is given as 7 inches.
2. Apply the formula:
[tex]\[
h = \frac{7 \cdot \sqrt{3}}{2}
\][/tex]
3. Calculate the height: Substitute the values into the formula and calculate the height.
[tex]\[
h = \frac{7 \cdot \sqrt{3}}{2} \approx \frac{7 \cdot 1.732}{2}
\][/tex]
Doing the multiplication first:
[tex]\[
7 \cdot 1.732 \approx 12.124
\][/tex]
Then divide by 2:
[tex]\[
\frac{12.124}{2} \approx 6.062
\][/tex]
4. Round the height to the nearest hundredth: The calculated height is approximately 6.062. When rounded to the nearest hundredth, the height is 6.06.
Thus, the height of the equilateral triangle with side lengths of 7 inches is approximately [tex]\(6.06\)[/tex] inches.
