Question

The lengths of two sides of a triangle are 6 centimetres and 4 centimetres; and the angle between them is 130°. What is its area?

Answer 1

Let the given triangle be ABC with AB = 4 cm, BC = 6 cm and ∠ABC = 130°.

Construction: Produce CB and draw AD perpendicular to CB produced.

By construction, we have ∠ADB = 90°

We know that the sum of angles of a linear pair is 180°.

∴ ∠ABC + ∠ABD = 180°

⇒ 130° + ∠ABD = 180°

⇒ ∠ABD = 180° − 130° = 50°

In ΔADB:

⇒ AD = AB × Sin 50° … (1)

We know that Sin 50° ≈ 0.7660 (From table)

Putting the value of Sin 50° in (1):

AD ≈ (4 × 0.7660) cm

= 3.064 cm

Area of a triangle =

Therefore, the area of ΔABC is approximately equal to 9.912 cm².