Question

AD is drawn perpendicular to BC, base of an equilateral triangle ABC. Given BC = 10 cm, find the length of AD, correct to 1 place of decimal.

Answer 1

if AD is a perpendicular to BC of Equilateral Triangle ABC then D is the midpoint of side BC ⇒ABD is a Right angled triangle

⇒ AD² + BD² = AB²

⇒ AD² = AB² - BD²

⇒ from the Triangle ABC

AB = 10 and BD = 5

substituting we get AD² = 100 - 25

AD² = 75

AD = √75 = 5√3 = 5 × 1.732 = 8.66m

So the height of AD is 8.66m