In triangle ABC, angle C is 90 degrees. ВС = 1 cosB = 1 \ √2. Find the AC.
| May 9, 2021 | education
The cosine of the angle is equal to the ratio of the adjacent leg to the hypotenuse, we express the cosine of the angle B: cosB = BC / AB.
Since cosB = 1 / √2, the equation is: 1 / AB = 1 / √2. Hence, AB = √2.
We calculate the length of the leg AC according to the Pythagorean theorem:
AB² = AC² + BC².
AC = √ (AB² – BC²) = √ ((√2) ² – 1²) = √ (2 – 1) = √1 = 1.
Answer: the length of the AC leg is 1.
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