Point M lies within an angle of 60 degrees. The distance from point M to each side of the angle is 5 cm. Find the distance from point M to the apex of the angle.
Let ∠A be given, MB = MC = 5 cm. It is necessary to find AM.
Since the distance from point M to each side ∠A is the same, it lies on the bisector ∠A. Thus, △ ABM = △ ACM, ∠MAB = ∠MAC = ∠A / 2 = 60 ° / 2 = 30 °.
Consider △ ACM: ∠ACM = 90 ° (since the distance from point M to side ∠A is a perpendicular), ∠MAC = 30 °, AM – hypotenuse, MC = 5 cm and AC – legs.
In a right-angled triangle, the leg, opposite an angle of 30 °, is equal to half the hypotenuse.
The MC leg lies opposite ∠MAC = 30 °, therefore MC = AM / 2.
AM / 2 = 5;
AM = 2 * 5 (proportional);
AM = 10 cm.
Answer: AM = 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.