Question
Download Solution PDFFind the lengths of the sides of a triangle, if its angles are in the ratio 1: 2: 3 and the circum-radius is 10 cm.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
- Sine Rule:
In a triangle Δ ABC, where a is the side opposite to A, b is the side opposite to B, c is the side opposite to C and where R is the circum-radius:
Calculation:
Given: Angles of a triangle are in the ratio 1: 2: 3 and the circum-radius is 10 cm.
Let A: B: C = 1: 2: 3 or A = k, B = 2k and C = 3k where k is any real number and R = 10 cm.
As we know that, A + B + C = 180°
⇒ A + B + C = k + 2k + 3k = 180°
⇒ k = 30°
⇒ A = 30°, B = 60° and C = 90°
As we know that,
⇒ a = 20 × sin 30° = 10 cm, b = 20 × sin 60° = 10√3 cm and c = 20 × sin 90° = 20 cm.
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