In a right-angled triangle ABC, the angle is C = 90, AB = 3, tgA = 0.75. Find BC.
May 22, 2021 | education
| The tangent of an angle is the ratio of the sine of that angle to the cosine.
tgA = SinA / CosA.
Since Sin ^ 2A + Cos ^ 2A = 1, then CosA = √ (1 – Sin ^ 2A).
tgA = SinA / √ (1 – Sin2A)
Let’s square both sides of the equation.
tg ^ 2A = Sin ^ 2A / (1 – Sin ^ 2A).
0.75 ^ 2 * (1 – Sin ^ 2A) = Sin ^ 2A.
(9/16) – (9/16) * Sin ^ 2A = Sin ^ 2A.
(25/16) * Sin ^ 2A = 9/16.
Sin ^ 2A = 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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