List the angles of TAG in order from largest to smallest of a T equals 12.5, GT equals 15.2 and AG equals 25.1

Answer 1

To find the angles of TAG, we can first use the Law of Cosines to find one of the angles. Then, we can use the Law of Sines to find the remaining two angles.

Using the Law of Cosines:
Given:
T = 12.5
G = 15.2
AG = 25.1

Let angle TAG be denoted as θ.
Using the Law of Cosines, we have:

T^2 + G^2 - 2T * G * cos(θ) = AG^2

(12.5)^2 + (15.2)^2 - 2(12.5)(15.2) * cos(θ) = (25.1)^2

156.25 + 231.04 - 381.28 * cos(θ) = 630.01

381.28 * cos(θ) = 387.29

cos(θ) = 387.29 / 381.28

θ ≈ arccos(1.0156) ≈ 8.88 degrees

Now, we can use the Law of Sines to find the remaining two angles.

sin(θ) / T = sin(TAG) / AG

sin(TAG) = (sin(θ) * AG) / T

sin(TAG) = (sin(8.88) * 25.1) / 12.5

sin(TAG) ≈ 0.143

So, TAG ≈ arcsin(0.143) ≈ 8.28 degrees

Since the sum of the angles in a triangle is 180 degrees, we can find the third angle:

Third angle = 180 - TAG - θ

Third angle = 180 - 8.28 - 8.88

Third angle ≈ 162.84 degrees

Therefore, the angles of TAG in order from largest to smallest are approximately:
- Third angle ≈ 162.84 degrees
- TAG ≈ 8.28 degrees
- θ ≈ 8.88 degrees