In an isosceles triangle ABC with base AC, the side AB is 25 and the height to the base is 20. Find the cosine of angle A.

univerkov | February 24, 2021 | education

Let VN be the height.

Consider a right-angled triangle ABH with right angle H.

Then, by the theorem of sines, BH = AB * sinA.

Therefore, sinA = BH / AB = 20/25 = 4/5.

Then, cosA = (1 – (sinA) ^ 2) ^ (1/2) = (1 – (4/5) ^ 2) ^ (1/2) = (1 – 16/25) ^ (1/2 ) = √ (9/25) = 3/5.

Answer: cosA = 0.6.

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