Find the base AC of an isosceles triangle ABC, in which the lateral side is 26√5 cm, and the sine

univerkov | September 25, 2021 | education

Find the base AC of an isosceles triangle ABC, in which the lateral side is 26√5 cm, and the sine of the angle at the base is 5/13.

Let’s build the height BH to the base of the speaker. Since the triangle ABC is isosceles, then BH is also the median and bisector of the triangle.

Determine the cosine of the angle BAC.

Cos2BAC = 1 – Sin2BAC = 1 – 25/169 = 144/169.

CosBAC = 12/13.

In a right-angled triangle ABC CosBAH = AH / AB.

AH = AB * CosBAH = 26 * √5 * 12/13 = 24 * √5 cm.

Then AC = 2 * AH = 2 * 24 * √5 = 48 * √5 cm.

Answer: The length of the base of the speaker is 48 * √5 cm.

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