In an isosceles triangle ABC with a base AC, the lateral side AB = 10, and the cosine of the angle A = 0.8. Find the height drawn to the base
Consider a triangle ABD.
By determining the cosine of an angle:
cos A = AD / AB;
AD = AB * cos A = 10 * 0.8 = 8.
By the Pythagorean theorem:
AB² = AD² + BD²;
BD² = AB² – AD² = 10² – 8² = 100 – 64 = 36.
BD = √ 36 = 6.
Answer: The height of the given isosceles triangle ABC is 6.
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