Question

order the sides from least to greatest *

bc, ab, ac
ab, ac, bc
ac, ab, bc
bc, ac, ab

Explanation:

Step1: Find the measure of angle \(C\)

In a right - angled triangle \(ABC\) with \(\angle B = 90^{\circ}\) and \(\angle A=38^{\circ}\), using the angle - sum property of a triangle (\(\angle A+\angle B+\angle C = 180^{\circ}\)).
Substitute \(\angle A = 38^{\circ}\) and \(\angle B = 90^{\circ}\) into the formula: \(38^{\circ}+90^{\circ}+\angle C=180^{\circ}\).
Then \(\angle C=180^{\circ}-(38^{\circ} + 90^{\circ})=52^{\circ}\).

Step2: Apply the side - angle relationship in a triangle

In a triangle, the side opposite the smaller angle is shorter.
The sides of the triangle are opposite the angles: side \(BC\) is opposite \(\angle A = 38^{\circ}\), side \(AB\) is opposite \(\angle C=52^{\circ}\), and side \(AC\) is opposite \(\angle B = 90^{\circ}\).
Since \(38^{\circ}<52^{\circ}<90^{\circ}\), the sides in order from least to greatest (using the side - opposite - angle relationship \(a/sinA=b/sinB = c/sinC\)): the side opposite \(38^{\circ}\) (\(BC\)), the side opposite \(52^{\circ}\) (\(AB\)), and the side opposite \(90^{\circ}\) (\(AC\)).

Answer:

BC, AB, AC