What is the height, x, of the equilateral triangle?
an equilateral triangle with the angles labeled as 60 degrees and a side length of 14 inches, the height labeled as x
In an equilateral triangle, all angles are equal to 60 degrees. The height of an equilateral triangle bisects the base and also creates a right triangle with the base. Let's use trigonometric ratios to find the height, x.
In the right triangle formed, the hypotenuse is the side of the equilateral triangle (14 inches) and the angle opposite the height is 60 degrees. Therefore, we can use the sine function:
sin(60) = opposite/hypotenuse
sin(60) = x/14
To find the value of sin(60), we can use the unit circle. The sine of 60 degrees is √3/2.
√3/2 = x/14
Multiplying both sides of the equation by 14:
14 * (√3/2) = x
7√3 = x
Therefore, the height of the equilateral triangle (x) is 7√3 inches.