In triangle ABC: ∠C = 90 °; BC = 2√6; AB = 2√30. Find tg∠A.
| March 18, 2021 | education
ABC is a right-angled triangle.
In a right-angled triangle, tg of an acute angle is equal to the ratio of the opposite leg to the adjacent leg.
Hence, tg A = BC / AC.
The length of the opposite BC leg is 2√6 (by condition).
To find tg A, you need to know the length of the AC side.
To do this, we use the Pythagorean theorem, according to which:
AC ^ 2 + BC ^ 2 = AB ^ 2.
AC ^ 2 = AB ^ 2 – BC ^ 2.
AC ^ 2 = (2√30) ^ 2 – (2√6) ^ 2 = 4 x 30 – 4 x 6 = 120 – 24 = 96.
AC = √96.
AC = √16 x 6.
AC = 4√6.
tg А = 2√6 / 4√6 = 1/2.
Answer: tg A is 1/2.
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