Question

Given: ΔАВС, m∠ACB = 90°

CD
⊥
AB
, m∠ACD = 60°,BC = 6 cm
Find CD, Area of ΔABC

Answer 1

Answer:

CD = 3√3 cm

area of ΔABC = 18√3 square cm

Step-by-step explanation:

If a right triangle having angles are 30, 60 and 90 then the sides are in the ratio 1:√3:2

Area of right triangle A = 1/2* base * height

From the figure attached with this answer

ΔABC is right triangle .

m∠ACB = 90°  m∠ACD = 60°,BC = 6 cm

To find CD

ΔBCD are right triangle

In  ΔBCD, m<D = 90°  (CD⊥AB)

m<C = 30°  and m<B= 60°  and BC = 6cm

Then BD : CD : BC = 3 : 3√3 : 6

Therefore CD = 3√3 cm

To find AC

ΔACD is right triangle.

m<C= 60° , m<A = 30° and m<D = 90°

CD : AD : AC =   3√3 : 9 : 6√3

AC = 6√3cm

To find area of  ΔABC

Area A = 1/2 * AC * CB= 1/2 * 6√3 * 6 = 18√3 square cm