Question

The law of cosines reduces to the Pythagorean theorem whenever the triangle is acute. true or false

Answer 1

False- the included angle must be a right angle for cos C to be 0 & two other points are normally used

Answer 2

Answer:

The given statement is False.

Step-by-step explanation:

Let us suppose a triangle ABC.

The law of cosine is given by

$c^2=a^2+b^2-2ab\cos C$

And the Pythagorean theorem is given by

$c^2=a^2+b^2$

Now, in order to the law of cosine to be in the form of Pythagorean theorem, we must have 2abcos C =0.

a and b can't be zero since it represent the sides of the triangle. Hence, we have

cos C= 0

thus, the value of C is 90 degrees. Hence, the triangle must be a right angle triangle.

Thus, the triangle shouldn't be acute triangle.

Therefore, the given statement is false/