Question

the sign for a new restaurant is an equilateral triangle with a height of 14 feet. what is the length of each side of the triangle, to the nearest tenth of a foot?

Answer 1

The length of each side of an equilateral triangle is equal to the square root of 3 times the length of its height. So, the length of each side of the sign is about 12.1 feet.

Here's the solution:

Let x be the length of each side of the triangle.

Since the triangle is equilateral, each angle is 60 degrees.

We can use the sine function to find the height of the triangle:

sin(60 degrees) = x/h

The sine of 60 degrees is sqrt(3)/2, so we have:

sqrt(3)/2 = x/h

h = x * sqrt(3)/2

We are given that h = 14 feet, so we can solve for x:

x = h * 2 / sqrt(3)

x = 14 feet * 2 / sqrt(3)

x = 12.1 feet (rounded to the nearest tenth)