The height AD of triangle ABC divides the side BC into segments BD and CD
| September 2, 2021 | education
The height AD of triangle ABC divides the side BC into segments BD and CD so that BD equals 15 cm; СD equals 5 cm Find the side АС if the angle B is 30 degrees.
Since AD is the height of triangle ABC, triangles ABD and ACD are rectangular.
In a right-angled triangle ABD through leg BD and angle ABD we determine the length of leg AD.
tgАВД = АD / ВD.
АD = ВD * tgАВD = 15 * (1 / √3) = 15 * √3 / 3 = 5 * √3 cm.
In a right-angled triangle AC, according to the Pythagorean theorem, we determine the length of the AC leg.
AC ^ 2 = AD ^ 2 + CD ^ 2 = (5 * √3) ^ 2 + 5 ^ 2 = 75 + 25 = 100.
AC = 10 cm.
Answer: The length of the speaker side is 10 cm.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.
