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Could you please help for this?
Please.

Could you please help for this? Please.-example-1
User Sapatos
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1 Answer

5 votes

Answer:

CD = 6.385 units

Explanation:

Given triangle ABC with right angle at C.

And AB = AD + 6 .

Now, consider the triangle ABC.

⇒ cos(∠BAC) =
(AC)/(AB) (cosФ = adj/hyp)

cos(20) =
(AC)/(AB) .

0.9397 =
(AD+CD)/(AD + 6)

(since AB = AD + 6 and AC = AD + CD)

⇒ 0.9397 AD + 5.6382 = AD + CD

CD = 0.0603 AD + 5.6382. →→→→→ (1)

⇒ sin(∠BAC) =
(BC)/(AB) (sinФ = opp/hyp)

sin(20) =
(BC)/(AB).

BC = AB sin(20) . →→→→→(2)

Now, consider the triangle BCD,

sin(∠BDC) =
(BC)/(CD)

⇒ sin(80) =
(BC)/(CD)

CD =
(BC)/(sin(80))

From (2), CD =
(AB sin(20))/(sin(80)) .

⇒ CD = AB (0.3473)

⇒ CD = (AD + 6) (0.3473)

CD = 0.3473 AD + 2.0838 →→→→→→(3)

Now, (1) →→ CD = 0.0603 AD + 5.6382

(3) →→ CD = 0.3473 AD + 2.0838

⇒ 0.0603 AD + 5.6382 = 0.3473 AD + 2.0838

0.287 AD = 3.5544.

⇒ AD = 12.3847

⇒ From (1), CD = 0.0603(12.3847) + 5.6382

CD = 6.385 units

User RAOF
by
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