Question

An equilateral triangle with side length 1 cm is shown in the diagram, work out the height of the triangle.

Give your answer rounded to 1 DP.

Answer 1

The height of the equilateral triangle is 2 cm.

Step-by-step explanation:

An equilateral triangle is a triangle with all sides of equal length and all angles measuring 60 degrees. In this case, the side length of the triangle is 1 cm. To find the height of the triangle, we can use the formula for the area of a triangle: 1/2 × base × height. Since the triangle is equilateral, the base is equal to the side length, which is 1 cm. To find the height, we can substitute the values into the formula and solve for height:

Area = 1/2 × 1 cm × height

1 cm² = 1/2 × height

height = 2 cm

Therefore, the height of the equilateral triangle is 2 cm.

Answer 2

0.9 cm

Step-by-step explanation:

c is the length of the side. a is the altitude. b is the base. a is the vertical bisector if the base, so the base is 0.5 cm.

c² = a² + b²

1² = a² + 0.5²

1² - 0.5² = a²

1 - 0.25 = a²

√0.75 = a

0.8660254 = a

round to 0.9