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.

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

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)