In triangle ABC, angle C is 90. AC = 15, AB = 5 √10. Find tgB.

univerkov | May 24, 2021 | education

By the Pythagorean theorem, we determine the length of the BC leg.

BC ^ 2 = AB ^ 2 – AC ^ 2 = (5 * √10) ^ 2 – 15 ^ 2 = 250 – 225 = 25.

BC = 5 cm.

Then tgABC = AC / BC = 15/3 = 3.

Second way.

Determine the sine of the angle ABC.

SinABC = AC / AB = 15 / (5 * √10) = 3 / √10.

Then Cos2ABC = 1 – Sin2ABC = 1 – 9/10 = 1/10.

CosABC = 1 / √10.

Then tgABC = SinABC / CosABC = (3 / √10) / (1 / √10) = 3.

Answer: The tangent of the angle ABC is 3.

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