List the angles of △TAG

Question

△
𝑇
𝐴
𝐺
in order from largest to smallest if AT=12.5
𝐴
𝑇
=
12.5
, GT=15.2
𝐺
𝑇
=
15.2
, and AG=25.1
𝐴
𝐺
=
25.1
.(1 point)
Responses

∠A
∠
𝐴
, ∠T
∠
𝑇
, ∠G
∠
𝐺
angle upper A , angle upper T , angle upper G

∠G
∠
𝐺
, ∠A
∠
𝐴
, ∠T
∠
𝑇
angle upper G , angle upper A , angle upper T

∠T
∠
𝑇
, ∠A
∠
𝐴
, ∠G
∠
𝐺
angle upper T , angle upper A , angle upper G

∠T
∠
𝑇
, ∠G
∠
𝐺
, ∠A

Answer 1

To determine the order of the angles in triangle \( \triangle TAG \) from largest to smallest based on the given side lengths, we can use the fact that in a triangle, the angle opposite the longest side is the largest, and the angle opposite the shortest side is the smallest.

The sides given are:

• \( AT = 12.5 \)
• \( GT = 15.2 \)
• \( AG = 25.1 \)

Now, let's identify which angle corresponds to which side:

• \( AG \) (25.1) is the longest side, which means \( \angle T \) is the largest angle.
• \( GT \) (15.2) is the second longest side, which means \( \angle A \) is the second largest angle.
• \( AT \) (12.5) is the shortest side, which means \( \angle G \) is the smallest angle.

Based on this, the order of the angles from largest to smallest is:

1. \( \angle T \)
2. \( \angle A \)
3. \( \angle G \)

The correct response is: ∠T, ∠A, ∠G (angle upper T, angle upper A, angle upper G).