Find the leg BC of a right-angled triangle ABC (angle B = 90) if AC = 12cm, cos C = 2/3.

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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