The height of a right-angled triangle, dropped from the top of the right angle, is 3. Angle A is 30 degrees
| August 14, 2021 | education
The height of a right-angled triangle, dropped from the top of the right angle, is 3. Angle A is 30 degrees. Find the legs and hypotenuse.
Since CH is the height of the ABC triangle, then the ACН triangle is also rectangular, then the length of the CH leg located opposite the angle 30 is equal to half the length of the AC.
CH = AC / 2, AC = 2 * CH = 2 * 3 = 6 cm.
In a right-angled triangle ABC tgBAC = BC / AC.
BC = AC * tg30 = 6 * √3 / 3 = 2 * √3 cm.
By the Pythagorean theorem, we determine the length of the hypotenuse AB.
AB ^ 2 = AC ^ 2 + BC ^ 2 = 36 + 12 = 48.
AB = 4 * √3 cm.
Answer: The lengths of the sides of the triangle are 6 cm, 2 * √3 cm, 4 * √3 cm.
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