Question

In ΔFGH, GH = 18, HF = 11, and FG = 8. Which list has the angles of ΔFGH in order from smallest to largest?
Answer
Multiple Choice Answers
m, angle, H, comma, m, angle, G, comma, m, angle, Fm∠H,m∠G,m∠F
m, angle, G, comma, m, angle, F, comma, m, angle, Hm∠G,m∠F,m∠H
m, angle, F, comma, m, angle, G, comma, m, angle, Hm∠F,m∠G,m∠H
m, angle, G, comma, m, angle, H, comma, m, angle, Fm∠G,m∠H,m∠F
m, angle, H, comma, m, angle, F, comma, m, angle, Gm∠H,m∠F,m∠G
m, angle, F, comma, m, angle, H, comma, m, angle, Gm∠F,m∠H,m∠G

Answer 1

To find the order of angles in triangle ΔFGH based on the lengths of the sides, we can use the property that the larger the side, the larger the opposite angle.

Given the lengths of the sides:
- GH = 18 (opposite to ∠F)
- HF = 11 (opposite to ∠G)
- FG = 8 (opposite to ∠H)

Now, we will arrange the sides from smallest to largest:
1. FG = 8 (smallest side)
2. HF = 11 (middle side)
3. GH = 18 (largest side)

Next, we will relate each side to its opposite angle:
- Side FG (8) is opposite to angle H (smallest angle).
- Side HF (11) is opposite to angle G (middle angle).
- Side GH (18) is opposite to angle F (largest angle).

Consequently, we have the following order for the angles:
m∠H < m∠G < m∠F

Thus, the angles of triangle ΔFGH in order from smallest to largest are:
m∠H, m∠G, m∠F.

The correct multiple-choice answer is:
**m∠H, m∠G, m∠F**.