Question

In Δ ABC, with the usual notations, if sin B sin C = `"bc"/"a"^2`, then the triangle is ______.

Options

• Right angled triangle

• Obtuse angled triangle

• Equilateral triangle

• Acute angled triangle

Answer 1

In Δ ABC, with the usual notations, if sin B sin C = `"bc"/"a"^2`, then the triangle is right angled triangle.

Explanation:

Use sine rule, i.e. `"a"/(sin "A") = "b"/(sin "B") = "c"/(sin "C")`

Given, sin B sin C = `"bc"/"a"^2`

`=> "a"^2 = "bc"/(sin "B"  sin "C")`

`=> "a"^2 = ("b"/(sin "B"))("c"/(sin "C"))`

`=> "a"^2 = ("a"/(sin "A"))^2`

⇒ sin² A = 1

⇒ sin A = 1 = sin 90°

⇒ A = 90°