Question

for a triangle base is 6√3 cm and two bases angles are 30 degree and 60 degree and height of the triangle is​

Answer 1

height of the triangle is 4.5 cm

given, base of a triangle = 6√3 cm

and two bases angles are 30° and 60°.

applying sine rule,

a/sinA = b/sinB = c/sinC

⇒ 6√3/sin90° = b/sin30° = c/sin60°

⇒6√3/1 = b/(1/2) = c/(√3/2)

a = 3√3 and b = 9

area of triangle = 1/2 × a × b = 1/2 × base × height

⇒3√3 × 9 = 6√3 × height

⇒9/2 = height

⇒height = 4.5 cm