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#
Question:

In triangle ABC, angle C is a right angle. If $9881_w75_h37.png$, what is the value of cos B?

A
$8917_w34_h41.png$

Explaination

If triangle ABC is defined as a right triangle, where angle C is the right angle, then the cosine of angle A (cos A) is defined as the ratio the *length of the side adjacent to angle A* ÷ *the length of the hypotenuse*. Since this ratio is defined as 5/8, then the the length of the hypotenuse length of the side opposite angle A, which is also the side adjacent to angle B, can be derived from the Pythagorean theorem: $6843_w101_h21.png$, where a represents the length of the side opposite angle A. Solving for a yields $2934_w147_h21.png$ so $7534_w73_h22.png$. Then, to determine the cosine of angle B, use the same ratio in relation to angle B:

cosB =* the length of the side adjacent to angle B*÷*the length of the hypotenuse* = $8917_w34_h41.png$.

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