Question

In Δ ABC; with usual notations, if cos A = `(sin "B")/(sin "C")`, then the triangle is _______.

Options

• Acute angled triangle

• Equilateral triangle

• Obtuse angled triangle

• Right angled triangle

Answer 1

In Δ ABC; with usual notations, if cos A = `(sin "B")/(sin "C")`, then the triangle is right angled triangle.

Explanation:

Use sine rule,

`(sin A)/"a" = (sin B)/"b" = (sin "C")/"c"`

We have,

cos A = `(sin "B")/(sin "C")`

`=> ("b"^2 + "c"^2 - "a"^2)/(2 "bc") = "b"/"c"   ...(because (sin "A")/"a" = (sin "B")/"b" = (sin "C")/"c" = "k")`

⇒ b² + c² - a² = 2b²

⇒ c² - a² = b²

⇒ c² = a² + b² 

⇒ Δ ABC right angled triangle at ∠C.