Question

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.

Answer 1

• 45°

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°