Find the leg BC of a right-angled triangle ABC (angle B = 90) if AC = 12cm, cos C = 2/3.
July 24, 2021 | education
| Find the leg BC of a right-angled triangle ABC (angle B = 90), if AC = 12 cm, cos C = 2/3.
Given:
triangle ABC,
angle B = 90 °,
AC = 12 cm,
cos C = 2/3.
Find: leg ВС -?
Solution :
ABC is a right-angled triangle, since the angle B = 90 ° (by condition), in which:
hypotenuse AC = 12 cm,
cos C = 2/3.
Let us recall what the cos of the angle in a right-angled triangle is equal to: cos of the angle is the ratio of the adjacent leg to the hypotenuse.
Consequently :
cos C = BC: AC,
2/3 = BC: 12,
BC = 12 * 2/3 = 8 cm.
Answer: the BC leg is 8 cm.
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