In the ABC triangle, the angle is C = 90, tgA = 8/15, BC = 4. Find AB.
February 5, 2021 | education
| Given a right-angled triangle ABC, angle C is 90 °, tan A = 8/15, BC = 4 cm. Find AB.
In a right-angled triangle, the tangent of an acute angle is equal to the ratio of the opposite leg to the adjacent leg, i.e.
tg A = BC / AC,
4 / AC = 8/15,
AC = (4 * 15) / 8 = 15/2.
By the Pythagorean theorem, we find the hypotenuse of the triangle:
AB ^ 2 = (15/2) ^ 2 + 4 ^ 2 = 225/4 + 16/1 = 289/4,
AB = 17/2.
Answer: 17/2.
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