An equilateral triangle has a height of 26 inches. What is the length of each side of the triangle to the nearest centimeter?
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
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
To find the length of each side of an equilateral triangle, you can use the Pythagorean theorem, which relates the height of an equilateral triangle to the length of each side.
The Pythagorean theorem states that the square of the length of the hypotenuse (in this case, a side of the triangle) is equal to the sum of the squares of the other two sides.
In an equilateral triangle, all three sides are equal in length, so we'll call the length of each side "s".
To find the length of each side, we can use the following formula:
s = √(h^2 + (s/2)^2)
Here, h represents the height of the triangle.
Plugging in the given values, we have:
s = √(26^2 + (s/2)^2)
Simplifying the equation, we get:
s^2 = 676 + (s^2/4)
Multiplying through by 4, we have:
4s^2 = 2704 + s^2
Combining like terms, we get:
3s^2 = 2704
Dividing through by 3, we find:
s^2 = 2704/3
Taking the square root of both sides, we get:
s = √(2704/3)
Approximating the square root and simplifying, we find the length of each side of the equilateral triangle to the nearest centimeter:
s ≈ 29.23 centimeters
To find the length of each side of the equilateral triangle, we can use the formula for the height of an equilateral triangle:
height = (√3/2) * side length
Given that the height is 26 inches, we can substitute the value into the formula and solve for the side length.
26 = (√3/2) * side length
To isolate the side length, we need to divide both sides of the equation by (√3/2):
side length = 26 / (√3/2)
Now we can simplify the expression:
side length = 26 * (2/√3)
To find the length of each side to the nearest centimeter, we need to convert inches to centimeters. Since 1 inch is equal to 2.54 centimeters, we can multiply the side length by 2.54:
side length (in centimeters) = (26 * (2/√3)) * 2.54
Now we can calculate the length of each side:
side length ≈ 44.868 centimeters
Therefore, the length of each side of the equilateral triangle, to the nearest centimeter, is approximately 44.868 centimeters.