Question

Let ABC be a triangle such that ∠A = 45°, ∠B = 75° then `"a" + "c"sqrt(2)` is equal to ______. (in usual notation)

Options

• 0

• b

• 2b

• –b

Answer 1

Let ABC be a triangle such that ∠A = 45°, ∠B = 75° then `"a" + "c"sqrt(2)` is equal to 2b. (in usual notation)

Explanation:

∵ `"a"/sin"A" = "b"/sin"B" = "c"/sin"C"`

⇒ `1/sin45^circ  = "b"/sin75^circ  = "c"/sin60^circ`

⇒ `sqrt() = (2sqrt(2))/(sqrt(3) + 1) = ""/sqrt(3)`

⇒ a = `(2"b")/(sqrt(3) + 1)`, c = `(sqrt(6)"b")/(sqrt(3) + 1)`

⇒ `"a" + "c"sqrt(2) = (2"b")/(sqrt(3) + 1) + (2"b"sqrt(3))/(sqrt(3) + 1)` = 2b