In a right-angled triangle ABC with right angle C, the tangent of the outer angle at the vertex A
| February 8, 2021 | education
In a right-angled triangle ABC with right angle C, the tangent of the outer angle at the vertex A is −3√10 / 20, side BC is 3. Find side AB.
The BAC angle is adjacent to the ВAD angle, the sum of which is 1800, then the BAC angle = (180 – ВAD).
tgBAC = tg (180 – BAD) = -tgBAC = 3 * √10 / 20.
The tangent of an acute angle of a right-angled triangle is equal to the ratio of the length of the opposite leg to the length of the adjacent leg.
tgВАС = ВС / АС.
АС = ВС / tgBAC = 3 / (3 * √10 / 20) = 20 / √10 = 2 * √10 cm.
In a right-angled triangle ABC, according to the Pythagorean theorem, AB^2 = BC^2 + AC^2 = 9 + 40 = 49.
AB = 7 cm.
Answer: The length of the hypotenuse AB is 7 cm.
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