In a right-angled triangle ABC, the angle is C = 90, AB = 3, tgA = 0.75. Find BC.

univerkov | May 10, 2021 | education

The tangent of an angle is the ratio of the sine of that angle to the cosine.

tgA = SinA / CosA.

Since Sin2A + Cos2A = 1, then CosA = √ (1 – Sin2A).

tgA = SinA / √ (1 – Sin2A)

Let’s square both sides of the equation.

tg2A = Sin2A / (1 – Sin2A).

0.752 * (1 – Sin2A) = Sin2A.

(9/16) – (9/16) * Sin2A = Sin2A.

25/16) * Sin2A = 9/16.

Sin2A = 9 * 16/16 * 25 = 9/25.

SinA = 3/5.

Then: SinA = BC / AB.

BC = AB * SinA = 3 * 3/5 = 9/5 = 1 (4/5) cm.

Answer: The length of the BC side is 1 (4/5) cm.

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