Find the Measure of Angles A & C in Triangle ABC

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SUMMARY

The discussion focuses on calculating the measures of angles A and C in triangle ABC with vertices A(-3,4), B(5,6), and C(2,1) using the tangent formula. The tangent of angle A is determined to be 1/4, leading to Angle A being arctan(1/4). Similarly, the tangent of angle C is calculated as 5/3, resulting in Angle C being arctan(5/3). The relationship between these angles and the total angle sum of 180 degrees is emphasized for verification.

PREREQUISITES
  • Understanding of trigonometric functions, specifically tangent and arctangent.
  • Familiarity with coordinate geometry and calculating slopes of lines.
  • Knowledge of angle properties in triangles, particularly the sum of angles.
  • Ability to perform basic arithmetic operations and manipulations with fractions.
NEXT STEPS
  • Learn how to apply the tangent formula in different geometric contexts.
  • Explore the properties of triangles, focusing on angle relationships and calculations.
  • Study coordinate geometry techniques for finding distances and angles between points.
  • Investigate the use of graphing tools to visualize geometric problems and solutions.
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Students studying geometry, mathematics educators, and anyone interested in applying trigonometric concepts to solve geometric problems.

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Using the formula relating the tangent of angle p enclosed between two given straight line L1 and L2 and respective slope m1 and m2,Find the measure in degrees of angles A and C of the triangle with vertices A(-3,4),B(5,6) and C(2,1)

My work is
Tan A = Ma = yb-ya/xb-xa=6-4/5+3=2/8=1/4
Tan A =1/4

Tan C = Mb = yb-yc/xb-xc=5/3
Tan C = 5/3

So Angle A = arctan 1/4
Angle C = arctan 5/3

Any idea on this?
 
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Those are the slopes of the lines and so give the angle each line makes with the horizontal.
For example, you have calculated, correctly, that the line from B to C makes an angle with the horizontal of arctan(5/3) and that the line from A to C makes an angle with the horizontal of arctan (5/3). Now draw a picture. You should see that the horizontal line through C makes 3 angles. The center is the angle C in the triangle. The arctangents are the other two angles. Use the fact that the total angle is 180 degrees (or pi radians).
 
yah I got u'r point
 

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