the lenght of a side of an equilateral triangle is 10m.find the height of the triangle
half of base = 5 m
hypotenuse = 10 m
h^2 + 5^2 = 10^2
h = sqrt (75)
To find the height of an equilateral triangle, we can use the Pythagorean theorem.
In an equilateral triangle, the height bisects the base, forming two right-angled triangles.
Let's label the length of the side of the triangle as "s" and the height as "h".
Using the Pythagorean theorem, we have:
s^2 = (h^2) + (s/2)^2
Plugging in the values given (s = 10m), we can rewrite the equation as:
(10^2) = h^2 + (10/2)^2
Simplifying:
100 = h^2 + 25
Rearranging to isolate h:
h^2 = 100 - 25
h^2 = 75
Taking the square root of both sides:
h = √75
Approximately:
h ≈ 8.66m
Therefore, the height of the equilateral triangle is approximately 8.66 meters.
To find the height of an equilateral triangle, you can use the formula:
Height = √3/2 × side length
Given that the side length of the equilateral triangle is 10m, we substitute this value into the formula:
Height = √3/2 × 10m
Now, let's simplify the calculation:
Height = √3/2 × 10m
Height = (1.732/2) × 10m
Height = 0.866 × 10m
Height = 8.66m
Therefore, the height of the equilateral triangle is 8.66 meters.