Trignometry Proof Help: Angle A < 60 Degrees

Thread starter Canada_Whiz
Start date Apr 8, 2010
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Proof Trignometry

In summary, to prove that angle A is less than 60 degrees, one can use trigonometric functions and the Pythagorean theorem to find the values of the sides of the triangle and compare the length of the hypotenuse to the length of one of the other sides. Other methods such as the law of cosines, law of sines, double angle formula, and half angle formula can also be used to prove this. To check the proof, one can use a calculator or trigonometric table, double check calculations, or seek feedback from others.

Apr 8, 2010

Canada_Whiz

Trignometry Proof Help!

If a,b,c are sides in a triangle such that a<1/2(b+c) show that angle A (the angle opposite to side a) is less than 60 degrees

Last edited: Apr 8, 2010

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Apr 8, 2010

mathman

Science Advisor

Have you tried the law of cosines?

a²=b²+c²-2bccosA

1. How can I prove that angle A is less than 60 degrees?

To prove that angle A is less than 60 degrees, you can use the trigonometric functions sine, cosine, and tangent to find the values of the sides of the triangle. Then, use the Pythagorean theorem to calculate the length of the hypotenuse. If the length of the hypotenuse is less than the length of one of the other sides, then angle A must be less than 60 degrees.

2. What steps should I follow to prove that angle A is less than 60 degrees?

First, draw a triangle with angle A as one of the angles. Then, use the trigonometric functions to find the values of the sides of the triangle. Next, use the Pythagorean theorem to calculate the length of the hypotenuse. Finally, compare the length of the hypotenuse to the length of one of the other sides to determine if angle A is less than 60 degrees.

3. Can I use the law of cosines to prove that angle A is less than 60 degrees?

Yes, you can use the law of cosines to prove that angle A is less than 60 degrees. The law of cosines states that c² = a² + b² - 2abcosC, where c is the length of the hypotenuse, a and b are the lengths of the other two sides, and C is the angle opposite the side c. If c² is less than the sum of a² and b², then angle A must be less than 60 degrees.

4. Are there any other methods to prove that angle A is less than 60 degrees?

Yes, there are other methods to prove that angle A is less than 60 degrees. You can use the law of sines, the double angle formula, or the half angle formula in combination with other trigonometric identities to prove that angle A is less than 60 degrees.

5. How can I check my proof that angle A is less than 60 degrees?

You can check your proof by using a calculator or a trigonometric table to verify the values of the sides and angles of the triangle. You can also double check your calculations and make sure that you followed all the necessary steps correctly. Additionally, you can ask a colleague or your teacher to review your proof and provide feedback.