Question

Could you please help for this? Please.

Answer 1

Answer:

CD = 6.385 units

Step-by-step explanation:

Given triangle ABC with right angle at C.

And AB = AD + 6 .

Now, consider the triangle ABC.

⇒ cos(∠BAC) = $\frac{AC}{AB}$  (cosФ = adj/hyp)

cos(20) = $\frac{AC}{AB}$ .

0.9397 = $\frac{AD+CD}{AD + 6}$

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

⇒ 0.9397 AD + 5.6382 = AD + CD

⇒ CD = 0.0603 AD + 5.6382. →→→→→ (1)

⇒ sin(∠BAC) =  $\frac{BC}{AB}$ (sinФ = opp/hyp)

sin(20) =  $\frac{BC}{AB}$.

⇒ BC = AB sin(20)  . →→→→→(2)

Now, consider the triangle BCD,

sin(∠BDC) =  $\frac{BC}{CD}$

⇒ sin(80) =  $\frac{BC}{CD}$

CD =  $\frac{BC}{sin(80)}$

From (2), CD = $\frac{AB sin(20)}{sin(80)}$ .

⇒ 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