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the diagram shows triangle ABC. D is on the point AB such that CD is perpendicular to AB. AC=9.4cm, AD=5.2cm and BD=7.8cm. Work out the size of angle ABC.

Respuesta :

mhanifa

Answer:

  • 45°

Step-by-step explanation:

Triangles ADC and BDC are right triangles, since CD⊥AB.

Use Pythagorean to find the length of CD:

  • CD² + AD² = AC²
  • CD² + 5.2² = 9.4²
  • CD² = 9.4² - 5.2²
  • CD² = 61.32
  • CD = √61.32
  • CD = 7.83

Use trigonometry to find the angle ABC:

  • tan (∠ABC) = CD/BD
  • tan (∠ABC) = 7.83/7.8
  • tan (∠ABC) = 1.0 (rounded)
  • m∠ABC = arctan 1
  • m∠ABC = 45°

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