Question

the front of the tent shown to the right has the shape of an equilateral triangle. a. what is the side length of the triangle? b. explain the method you use to calculate the length. a. the side length of the triangle is (type an integer or decimal rounded to the nearest tenth as needed.)

Explanation:

Step1: Recall property of equilateral triangle

In an equilateral triangle, if the height (altitude) is \(h\) and the side - length is \(s\), the relationship between the height and the side - length is given by \(h=\frac{\sqrt{3}}{2}s\). Here, \(h = 5\) ft.

Step2: Solve for side - length \(s\)

From \(h=\frac{\sqrt{3}}{2}s\), we can re - arrange the formula to solve for \(s\). We get \(s=\frac{2h}{\sqrt{3}}\). Substitute \(h = 5\) into the formula: \(s=\frac{2\times5}{\sqrt{3}}=\frac{10}{\sqrt{3}}\). Rationalize the denominator: \(s=\frac{10\sqrt{3}}{3}\approx\frac{10\times1.732}{3}=\frac{17.32}{3}\approx5.8\) ft.

Answer:

a. \(5.8\)
b. We use the property that for an equilateral triangle, the height \(h\) and side - length \(s\) are related by \(h = \frac{\sqrt{3}}{2}s\). We re - arrange the formula to \(s=\frac{2h}{\sqrt{3}}\), substitute the given height \(h = 5\) ft, and then rationalize the denominator to find the side - length.