Question

What’s the angle of cda

Answer 1

∠ CDA = 32.3°

Explanation:

See the given figure attached to this answer.

Draw perpendiculars from B and C on AD which is BE and CF.

Now, Δ ABE is a right triangle and AE² = AB² - BE² = 7.5² - 6² = 20.25

⇒ AE = 4.5 cm

Now, DF = AD - EF - AE = 24 - 10 - 4.5 = 9.5 cm {Since BC = EF}

And CF = BE = 6 cm.

Now, Δ CFD is a right triangle and

`\tan \beta  =(CF)/(FD) = (6)/(9.5)  = 0.6315` {Where β = ∠ CDA}

⇒
`\beta  = \tan^(-1) (0.6315)=32.27` Degree.

So, ∠ CDA = 32.3° {Correct to one decimal place} (Answer)