According to the Pythagorean theorem, in the right-angled triangle ABC, we determine the length of the leg BC.
BC ^ 2 = AB ^ 2 – AC ^ 2 = 1600 – 1024 = 576.
BC = 24 cm.
Then tgBAC = BC / AC = 24/32 = 0.75.
Determine the cosine of the angle BAC.
CosBAC = AC / AB = 32/40 = 0.8.
Determine the sine of the angle BAC.
Sin2BAC = 1 – Cos2BAC = 1 – 0.64 = 0.36.
SinBAC = 0.6.
Then tgBAC = SinBAC / CosBAC = 0.6 / 0.8 = 0.75.
Answer: The tangent of the angle BAC is 0.75.
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