Find the Measure of Angles A & C in Triangle ABC

In summary, the formula for finding the measure of angles A and C in a triangle with vertices A(-3,4), B(5,6), and C(2,1) can be found by using the tangent of angle p, which is enclosed between two given straight lines L1 and L2 with respective slopes m1 and m2. After plugging in the given coordinates, it is determined that the measure of angle A is arctan(1/4) and the measure of angle C is arctan(5/3). By drawing a picture and using the fact that the total angle is 180 degrees, it can be seen that the horizontal line through C makes 3 angles, with angle C being the
  • #1
kidia
66
0
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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  • #2
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).
 
  • #3
yah I got u'r point
 

FAQ: Find the Measure of Angles A & C in Triangle ABC

How do you find the measure of angle A in Triangle ABC?

The measure of angle A can be found by using the Law of Cosines or the Law of Sines, depending on the information given about the triangle. If the lengths of all three sides are known, the Law of Cosines can be used. If the lengths of two sides and the measure of the included angle are known, the Law of Sines can be used.

What is the relationship between the measures of angles A and C in Triangle ABC?

In a triangle, the sum of all three angles is always 180 degrees. This means that angle A and angle C are complementary, meaning they add up to 90 degrees. This relationship holds true for all triangles, regardless of their shape or size.

Can the measure of angle A in Triangle ABC be greater than 90 degrees?

No, the measure of angle A cannot be greater than 90 degrees. In a triangle, the largest angle is always opposite the longest side. If the measure of angle A were greater than 90 degrees, it would mean that the side opposite it is longer than the longest side, which is not possible.

How do you find the measure of angle C in Triangle ABC if the measure of angle A is known?

The measure of angle C can be found by subtracting the measure of angle A from 180 degrees. Since angles A and C are complementary, they add up to 90 degrees, and 90 degrees added to 90 degrees is 180 degrees.

Is it possible to find the measure of angles A and C in Triangle ABC if the lengths of all three sides are known?

Yes, it is possible to find the measure of angles A and C in Triangle ABC if the lengths of all three sides are known. As mentioned before, the Law of Cosines can be used to find the measures of these angles. However, there may be multiple solutions, as a triangle can have different angle measurements but still have the same side lengths.

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