Problem

Use vectors to find the interior angles of the triangle given the following sets of vertices. Round your answer, in degrees, \[ (7,0),(-7,5),(-1,-8) \]

Solution

Step 1 :Given the vertices of the triangle A = (7, 0), B = (-7, 5), and C = (-1, -8).

Step 2 :Calculate the vectors AB, BC, and CA. AB = B - A = (-14, 5), BC = C - B = (6, -13), and CA = A - C = (8, 8).

Step 3 :Calculate the magnitudes of these vectors. The magnitude of AB is approximately 14.87, the magnitude of BC is approximately 14.32, and the magnitude of CA is approximately 11.31.

Step 4 :Calculate the dot products of the vectors. The dot product of AB and BC is -149, the dot product of BC and CA is -56, and the dot product of CA and AB is -72.

Step 5 :Use the dot product formula to find the angles. The angle between AB and BC is approximately \(134^\circ\), the angle between BC and CA is approximately \(110^\circ\), and the angle between CA and AB is approximately \(115^\circ\).

Step 6 :Final Answer: The interior angles of the triangle are approximately \(\boxed{134^\circ}\), \(\boxed{110^\circ}\), and \(\boxed{115^\circ}\).

From Solvely APP
Source: https://solvelyapp.com/problems/xliK3rtvA0/

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