Question

In triangle ABC, angle B is a right angle. The coordinates for each point are A (10,7), B (5,9), and C (3,4). What is the measure of angle A?

1) 45 degrees
2) 60 degrees
3) 90 degrees
4) 120 degrees

Answer 1

To find the measure of angle A in triangle ABC, we can use trigonometry. By calculating the lengths of the sides and using trigonometric ratios, we can determine that the measure of angle A is 45 degrees.

Step-by-step explanation:

To find the measure of angle A in triangle ABC, where angle B is a right angle, we can use the concept of trigonometry. We know the coordinates of points A, B, and C, so we can calculate the lengths of the sides of the triangle. From that, we can use trigonometric ratios to find the measure of angle A.

First, we find the lengths of the sides AB and BC using the distance formula. AB = sqrt((10-5)^2 + (7-9)^2) = sqrt(25+4) = sqrt(29), BC = sqrt((3-5)^2 + (4-9)^2) = sqrt(4+25) = sqrt(29).

Next, we can use the tangent function to find the measure of angle A. tan(A) = opposite/adjacent = BC/AB = sqrt(29)/sqrt(29) = 1. Therefore, the measure of angle A is 45 degrees.