Question

в треугольнике MNK MN=NK,MK=2в корне,угол M=30,MA-биссектриса.найти MA.

Answer 1

треугольник МНК равнобедренный, МН=НК, уголМ=уголК=30, уголН=180-30-30=120, МК=корень2, MK/sin120=HK/sin30, корень2/(корень3/2)=НК/(1/2), НК=2*корень2/2*корень3=корень6/3=МН, треугольник МАН, уголНМА=уголМ/2=30/2=15, уголМАН=180-120-15=45, МН/sin45=МА/sin120, (корень6/3) / (корень2/2) =МА/(корень3/2), МА=(2*корень6*корень3)/(3*корень2*2)=1

Answer 2

Given Information:

We are given the following information about triangle MNK: - MN = NK - MK = 2√3 - ∠M = 30° - MA is the bisector of angle M.

Solution:

To find the length of MA, we can use the angle bisector theorem. According to this theorem, the length of MA can be found using the formula:

MA = (MN * MK) / (MN + NK)

Let's substitute the given values into the formula and calculate the length of MA.

Substituting MN = NK, we can rewrite the formula as:

MA = (MN * MK) / (2 * MN)

Since MN = NK, we can simplify the formula further:

MA = MK / 2

Substituting MK = 2√3, we get:

MA = (2√3) / 2 = √3

Therefore, the length of MA is √3.

Please let me know if I can help you with anything else.