ECZ 2010 · O-Level Paper 2 · Question 5 — Trigonometry

In the diagram below, triangles ABC and ACD are right angled. Angle ABC = angle CAD = 90°, AC = 20.2 cm, BC = 9.5 cm and AD = 12 cm. Calculate

(a) AB,[2]

Verified working — step 1

Triangle ABC is right-angled at B, so AC is the hypotenuse.

(b) angle BAC,[2]

Verified working — step 1

BC is opposite angle BAC and AC is the hypotenuse, so use sine.

(c) the area of quadrilateral ABCD,[3]

Verified working — step 1

Split the quadrilateral into the two right-angled triangles.

(d) the perimeter of quadrilateral ABCD.[3]

Verified working — step 1

Triangle ACD is right-angled at A, so CD is its hypotenuse.

The full step-by-step working and final answer are included with Premium — checked against ECZ marking standards.

Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

Have a different question?

Search it — if it is from a past paper or a school mock, chances are we have it worked out, or one that uses the same method.