MYP Extended Mathematics 7.2 Sine Rule Questionbank

In triangle $ABC$, $A = 30^\circ$, side $b = 10$, and side $a = 12$. How many distinct triangles can be formed with these dimensions?

A surveyor identifies a triangle $ABC$ where side $AB = 100$ m, side $BC = 60$ m, and angle $A = 30^\circ$. How many distinct triangles can be formed with these specific dimensions?

$h = b \sin A$ and $h = b \sin C$

$h = c \sin A$ and $h = a \sin C$

$h = a \sin A$ and $h = c \sin C$

$h = c \cos A$ and $h = a \cos C$

No such triangle exists

Exactly two triangles exist

The triangle is equilateral

Exactly one right-angled triangle exists

Because an obtuse angle can only exist in a triangle if all three side lengths are known.

Because the shortest side of a triangle must always be opposite the largest interior angle.

Because the side opposite the largest angle must be the longest side, but here $b < a$.

Because the sine rule requires that the unknown angle must always be smaller than the given angle.