Question

To find the angle AGD in the triangle with vertices (-6,2), (5,4), and (5,0), you can use trigonometry.

1. First, find the lengths of the sides AG, GD, and AD using the distance formula between the given coordinates.
2. Then, use the law of cosines to find the angle AGD.

Answer 1

To find the angle AGD in the triangle with vertices (-6,2), (5,4), and (5,0), you can use trigonometry. First, find the lengths of the sides AG, GD, and AD using the distance formula. Then, use the law of cosines to find the angle AGD, which is approximately 53.1°.

Step-by-step explanation:

To find the angle AGD in the triangle with vertices (-6,2), (5,4), and (5,0), you can use trigonometry. Here are the steps:

1. Find the lengths of the sides AG, GD, and AD using the distance formula between the given coordinates.
2. Use the law of cosines to find the angle AGD.

Applying these steps to the given coordinates:

• AG = sqrt[(-6-5)^2 + (2-4)^2] = sqrt[121 + 4] = sqrt(125)
• GD = sqrt[(5-5)^2 + (4-0)^2] = sqrt[0 + 16] = 4
• AD = sqrt[(-6-5)^2 + (2-0)^2] = sqrt[121 + 4] = sqrt(125)

Using the law of cosines, we can find the angle AGD:

cos(AGD) = (AG^2 + GD^2 - AD^2) / (2 * AG * GD)

cos(AGD) = (125 + 4 - 125) / (2 * sqrt(125) * 4)

cos(AGD) = 4 / (2 * sqrt(125) * 4)

cos(AGD) = 1 / (2 * sqrt(125))

AGD = arccos(1 / (2 * sqrt(125)))

AGD ≈ 53.1°