Chapter 0.2, Problem 2E

(a)

To determine

To find: The height $h$ of an equilateral triangle as a function of its length $s$ .

Answer to Problem 2E

The height $h$ of an equilateral triangle as a function of its length $s$ is equal to $\frac{\sqrt{3}}{2}s$ .

Explanation of Solution

Given information:

The side of the equilateral triangle is $s$ .

Calculation:

The height $h$ of an equilateral triangle is given by

  $h=\frac{\sqrt{3}}{2}s$ , where $s$ is a side of the equilateral triangle.

Therefore, the height $h$ of an equilateral triangle as a function of its side $s$ is $\frac{\sqrt{3}}{2}s$ .

(b)

To determine

To find: The height of an equilateral triangle.

Answer to Problem 2E

The height of an equilateral triangle is equal to $\frac{3\sqrt{3}}{2}$ m.

Explanation of Solution

Given information:

The side of the equilateral triangle is $3$ m.

Calculation:

From the part (a),

The height $h$ of an equilateral triangle is $\frac{\sqrt{3}}{2}s$ .

Since the side length is $3$ m, so the height of the equilateral triangle is below:

  $\begin{array}{c}h=\frac{\sqrt{3}}{2}\times 3\\ =\frac{3\sqrt{3}}{2}\\ =4\pi \end{array}$

Therefore, the height of the equilateral triangle is $\frac{3\sqrt{3}}{2}$ meters.