Given: δавс, m∠acb = 90°

cd
⊥
ab
, m∠acd = 60°,bc = 6 cm
find cd, area of δabc

CD = 5.196 cm

Area = 31.177 sq. cm.

Step-by-step explanation:

See the attached diagram.

Given that ∠ ACB = 90° in Δ ABC.

Now, CD ⊥ AB and ∠ CDB = ∠ CDA = 90°

Given that ∠ ACD = 60° and BC = 6 cm.

We have to find the length of CD and the area of Δ ABC.

Now, ∠ CAD = 90° - ∠ ACD = 90° - 60° = 30°  

Again, ∠ CBD = 90° - ∠ CAD = 90° - 30° = 60°.

Now, from Δ BCD,

{Since Δ BCD is a right triangle and ∠ CDB = 90°}  

⇒ cm. (Answer)

Now, from Δ ACD,

{Since Δ ACD is a right triangle and ∠ ADC = 90°}

⇒ cm

So, the area of Δ ABC = sq. cm. (Answer)

the anwser is d) 75°

step-by-step explanation: