Question

13.

DFT has vertices D(3,-2), F(5, 1), and T(-2, 4). List the angles of this triangle in order from least to
greatest.

Answer 1

Explanation:

To find the angles of the DFT triangle in order from least to greatest, we can use the law of cosines.

Let's first find the lengths of the sides of the triangle using the distance formula:

DF = sqrt[(5 - 3)^2 + (1 - (-2))^2] = sqrt(29)

FT = sqrt[(-2 - 5)^2 + (4 - 1)^2] = sqrt(74)

DT = sqrt[(3 - (-2))^2 + (-2 - 4)^2] = sqrt(74)

Now, we can use the law of cosines to find the angles:

Angle D: cos(D) = (DF^2 + DT^2 - FT^2) / (2 * DF * DT) = (29 + 74 - 74) / (2 * sqrt(29) * sqrt(74)) = 0, so angle D is 90 degrees.

Angle F: cos(F) = (DF^2 + FT^2 - DT^2) / (2 * DF * FT) = (29 + 74 - 29) / (2 * sqrt(29) * sqrt(29)) = 1, so angle F is 0 degrees.

Angle T: cos(T) = (DT^2 + FT^2 - DF^2) / (2 * DT * FT) = (74 + 29 - 74) / (2 * sqrt(74) * sqrt(29)) = 5 / (2 * sqrt(74) * sqrt(29)), so we need to use the inverse cosine function to find the angle: T = cos^-1(5 / (2 * sqrt(74) * sqrt(29))) = 52.8 degrees.

Therefore, the angles of the DFT triangle in order from least to greatest are F (0 degrees), D (90 degrees), and T (52.8 degrees)