Question

1
select the correct answer from each drop - down menu.
in triangle abc, (mangle a = 36^{circ}), (mangle b = 84^{circ}), and (mangle c = 60^{circ}).
the side lengths, in order from greatest to least, are
(the drop - down menu options are ab, ac, bc)
(there are also reset and next buttons)

Explanation:

Step1: Recall the triangle side-angle relationship

In a triangle, the longer side is opposite the larger angle. So we first identify the angles and their opposite sides.

• Angle \( A = 36^\circ \), opposite side \( BC \)
• Angle \( B = 84^\circ \), opposite side \( AC \)
• Angle \( C = 60^\circ \), opposite side \( AB \)

Step2: Order the angles from largest to smallest

The angles in order from largest to smallest: \( \angle B = 84^\circ \), \( \angle C = 60^\circ \), \( \angle A = 36^\circ \)

Step3: Determine the order of the sides (opposite the angles)

Since the side opposite the larger angle is longer, the sides opposite the angles (in order of largest to smallest angles) will be in order of longest to shortest.

• Opposite \( \angle B \) (largest angle) is \( AC \)
• Opposite \( \angle C \) is \( AB \)
• Opposite \( \angle A \) (smallest angle) is \( BC \)

So the side lengths in order from greatest to least are \( AC \), \( AB \), \( BC \)

Answer:

\( AC \), \( AB \), \( BC \)