The definition of theorem?

Mathematics

1 answer:

charle [14.2K]2 years ago

5 0

Answer:

In mathematics, a theorem is a non-self-evident statement that has been proven to be true, either on the basis of generally accepted statements such as axioms or on the basis of previously established statements such as other theorems. A theorem is hence a logical consequence of the axioms, with a proof of the theorem being a logical argument which establishes its truth through the inference rules of a deductive system. As a result, the proof of a theorem is often interpreted as justification of the truth of the theorem statement. In light of the requirement that theorems be proved, the concept of a theorem is fundamentally deductive, in contrast to the notion of a scientific law, which is experimental.

Step-by-step explanation:

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Answer:

$\sf \tan(A) & =\dfrac{9\sqrt{22}}{44}$

Step-by-step explanation:

If angle C is the right angle, then side c is the hypotenuse.

Use Pythagoras' Theorem $a^2+b^2=c^2$ to find the length of side a:

Given:

b = 2√22
c = 13

$\implies a^2+(2 \sqrt{22})^2=13^2$

$\implies a^2+88=169$

$\implies a^2=81$

$\implies a=\sqrt{81}$

$\implies a=9$

<u>Tan Trig Ratio</u>

$\sf \tan(\theta)=\dfrac{O}{A}$

where:

$\theta$ is the angle
O is the side opposite the angle
A is the side adjacent the angle

Given:

$\theta$ = A
O = side opposite angle A = a = 9
A = side adjacent angle A = b = 2√22

$\begin{aligned}\implies \sf \tan(A) & =\dfrac{9}{2\sqrt{22}}\\\\ & =\dfrac{9}{2\sqrt{22}} \times \dfrac{\sqrt{22}}{\sqrt{22}}\\\\ & = \dfrac{9\sqrt{22}}{44} \end{aligned}$