Question

In a triangle the length of the two larger sides are 10 and 9, respectively. If the angles are in A.P., then the length of the third side can be ______.

Options

• 9.52

• 9.53

• 9.54

• 9.55

Answer 1

In a triangle the length of the two larger sides are 10 and 9, respectively. If the angles are in A.P., then the length of the third side can be 9.54.

Explanation:

Since, angles of Δ are in AP.

⇒ (α – δ) + α + (α + δ) = 180°

⇒ α = 60°

Let, third side is x.

Using cosine law in ΔABC

cos 60° = `((10)^2 + (9)^2 - x^2)/(2.(10).(9))`

⇒ `1/2 = (181 - x^2)/(2.(90))`

⇒ x² = 91

⇒ x = `sqrt(91)`

⇒ x = 9.54