alphabets
Answered

Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

AB and DC are parallel.

Work out the area of the triangle BCD.
Give your answer correct to 3 significant figures.

AB And DC Are Parallel Work Out The Area Of The Triangle BCD Give Your Answer Correct To 3 Significant Figures class=

Sagot :

sqdancefan

Answer:

  583 cm²

Step-by-step explanation:

To find the area of triangle BCD, we need to know the length of segment BD. That can be found from the law of sines:

  BD/sin(A) = BA/sin(D)

  BD = (sin(A)/sin(D))BA = sin(70°)/sin(74°)·(39 cm) ≈ 38.1249 cm

Then the area of BCD is ...

  A = 1/2(DB)(DC)sin(BDC)

Angle BDC, together with the marked angles, makes a total of 180°.

 ∠BDC = 180° -74° -70° = 36°

  A = 1/2)(38.1249 cm)(52 cm)sin(36°) ≈ 582.64 cm² ≈ 583 cm²

_____

Additional comment

The angle relation we used comes from the fact that consecutive interior angles where a transversal crosses parallel lines are supplementary. That means angle DAB and ADC are supplementary. Angle ADC is the sum of angles ADB and BDC, so we have ...

  ∠DAB +∠ADB +∠BDC = 180°

  ∠BDC = 180° -∠DAB -∠ADB

Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.