Question

list the angles of the triangle in order from smallest to largest. note that the figure is not drawn to scale. choose the correct order of the angles from smallest to largest. a. ∠l, ∠m, ∠k b. ∠l, ∠k, ∠m c. ∠k, ∠m, ∠l d. ∠m, ∠k, ∠l e. ∠k, ∠l, ∠m f. ∠m, ∠l, ∠k

Explanation:

Step1: Find the length of the third side

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) (where \(a = 2.3\), \(b=2.9\), and \(c\) is the hypotenuse). But we can also use the property that in a triangle, the larger the side, the larger the angle opposite it.
The side lengths: \(MK = 2.9\), \(ML=2.3\), and by Pythagorean theorem \(LK=\sqrt{2.3^{2}+2.9^{2}}=\sqrt{5.29 + 8.41}=\sqrt{13.7}\approx3.7\)

Step2: Relate side lengths and angles

In \(\triangle MLK\), the side - angle relationship: the angle opposite the shorter side is smaller.
The side lengths in ascending order: \(ML = 2.3\), \(MK=2.9\), \(LK\approx3.7\)
The angles opposite these sides: \(\angle K\) (opposite \(ML\)), \(\angle L\) (opposite \(MK\)), \(\angle M\) (opposite \(LK\))

So the angles from smallest to largest: \(\angle K\), \(\angle L\), \(\angle M\)

Answer:

E. $\angle K$, $\angle L$, $\angle M$