Question

One angle of a right angled triangle is 30° and its hypotenuse is 4 centimetres. What is its area?

Answer 1

Let ΔABC be the given right-angled triangle, right-angled at B.

Also, ∠ACB = 30° and Hypotenuse = AC = 4 cm

Using angle sum property in ΔABC:

∠ABC + ∠BCA + ∠CAB = 180°

⇒ 90° + 30° + ∠CAB = 180°

⇒ 120° + ∠CAB = 180°

⇒ ∠CAB = 180° − 120° = 60°

Thus, the angles of ΔABC are 30°, 60° and 90°.

Therefore, the ratio of the lengths of the sides of ΔABC is 1::2.