# In a triangle ABC AC = BC = 2√17, AB = 16 Find the tangent of angle A

October 12, 2021 | education

| Since AC = BC, triangle ABC is isosceles with base AB.

From the top of C to the base of AB, we construct the height CH, which is also the median and bisector of the triangle ABC, then AH = BH = AB / 2 = 16/2 = 8 cm.

In a right-angled triangle ACH, according to the Pythagorean theorem, we determine the length of the leg CH.

CH ^ 2 = AC ^ 2 – AH ^ 2 = 68 – 64 = 4.

CH = 2 cm.

Then tgCAB = CH / AH = 2/8 = 1/4 = 0.25.

Answer: The tangent of angle A is 0.25.

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