An equilateral triangle has a height of 26 inches. What is the length of each side of the triangle to the nearest centimeter?

Answer 1

In an equilateral triangle :

h = a * sqrt ( 3 ) / 2

26 = a * sqrt ( 3 ) / 2 Multiply both sides by 2

26 * 2 = a * sqrt ( 3 )

52 = a * sqrt ( 3 ) divide both sides by sqrt ( 3 )

52 / sqrt ( 3 ) = a

52 / 1.73205 = a

30.022228 in = a

a = 30.022228 in

1 in = 2.54 cm

a = 30.022228 * 2.54 =

a = 76.25645912 cm

a = 76 cm to the nearest centimeter

Answer 2

You should have learned that the ratio of sides of an
30-60-90 triangle is
1 : √3 : 2

x/2 = 26/√3
x = 52/√3 = 30.0222 or appr 30 cm

or
sin 60 = 26/x
x = 26/sin60 = 30.0222