Question

The sides of a triangle be three consecutive natural number such that its largest angle is twice the smallest. Then the value of the least side is​

Answer 1

Answer:

5

Step-by-step explanation:

Using sine law,

n−1sinα=n+1sin2α

⇒2cosα=(n−1)n+1

⇒cosα=2(n−1)n+1

∴2n(n+1)n2+(n+1)2−(n−1)2=2(n−1)(n+1) (using cosine law)

⇒2n+(n+1)n2+4n=2(n−1)(n+1)

⇒2(n+1)n+4=2(n−1)n+1

(n+1)⇒2(n+1)n+4=2(n−1)n+1⇒(n+1)2=(n+1⇒2n+(n+1)n2+4n=2(n−1)(n+1)

⇒2(n+1)n+4=2(n−1)n+1

∴n=5

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