Finding Angle C in Triangle ABC

In summary, to find the measure of angle C in Triangle ABC, you can use either the Law of Cosines or the Law of Sines. The Pythagorean Theorem cannot be used for this purpose since it only applies to right triangles. The formula for finding angle C using the Law of Cosines is cos(C) = (a^2 + b^2 - c^2) / (2ab), where a and b are the lengths of two sides and c is the length of the remaining side. Depending on the given information, there can be one or two solutions for finding angle C. The Law of Sines requires at least two side lengths and one angle measurement to find the measure of an angle in a triangle,
  • #1
Albert1
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$\triangle ABC,\angle B=30^o , \,\,and \,\, \overline{BC}^2 - \overline{AB}^2=\overline{AB}\times \overline{AC}\\
find \,\, \angle C=?$
 
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  • #2
Albert said:
$\triangle ABC,\angle B=30^o , \,\,and \,\, \overline{BC}^2 - \overline{AB}^2=\overline{AB}\times \overline{AC}\\
find \,\, \angle C=?$
hint
prove $\angle A=2\angle C$
 
  • #3
Albert said:
$\triangle ABC,\angle B=30^o , \,\,and \,\, \overline{BC}^2 - \overline{AB}^2=\overline{AB}\times \overline{AC}---(1)\\
find \,\, \angle C=?$
more hint:
in fact $\angle B=30^o$ is not important, you should prove for any triangle if $\angle A=2\angle C $ then (1) will meet
 
  • #4
Albert said:
more hint:
in fact $\angle B=30^o$ is not important, you should prove for any triangle if $\angle A=2\angle C $ then (1) will meet
my solution :
View attachment 5446
 

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Related to Finding Angle C in Triangle ABC

1. How do I find the measure of angle C in Triangle ABC?

To find the measure of angle C in Triangle ABC, you can use the Law of Cosines or the Law of Sines. You will need to know the lengths of at least two sides of the triangle and one angle measurement.

2. Can I use the Pythagorean Theorem to find angle C in Triangle ABC?

No, the Pythagorean Theorem can only be used to find the length of sides in a right triangle. Since Triangle ABC is not specified as a right triangle, the Pythagorean Theorem cannot be used to find the measure of angle C.

3. What is the formula for finding angle C in Triangle ABC using the Law of Cosines?

The formula for finding angle C in Triangle ABC using the Law of Cosines is: cos(C) = (a^2 + b^2 - c^2) / (2ab), where a and b are the lengths of two sides of the triangle, and c is the length of the remaining side.

4. How many solutions can there be for finding angle C in Triangle ABC?

There can be either one or two solutions for finding angle C in Triangle ABC. If the given information is enough to determine a unique triangle, then there will be one solution. If the given information can result in two different triangles, then there will be two solutions.

5. Can I use the Law of Sines to find angle C in Triangle ABC if I only know the length of one side?

No, the Law of Sines requires at least two side lengths and one angle measurement to find the measure of an angle in a triangle. If you only know the length of one side, you will not have enough information to use the Law of Sines to find angle C in Triangle ABC.

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