Question

Дан треугольник MKD. MK 4см, MD 8 см, KD 6см. Найти косинус угла M и сам угол М

Answer 1

теорема косинусов   а^2=b^2+C^2-2BC*COSL   ОПРЕДЕЛЯЕМ COS M=(MD^2+MK^2-KD^2)/2*MD*MK=(64+16-36)2*4*8=11/16=0.687 УГОЛ ПО ТАБЛИЦЕ

Answer 2

Finding the Cosine of Angle M and Angle M in Triangle MKD

To find the cosine of angle M and the angle M in triangle MKD, we can use the cosine rule, which states that for any triangle with sides a, b, and c, and angle C opposite side c, the following equation holds true:

c^2 = a^2 + b^2 - 2ab * cos(C)

Given: - MK = 4 cm - MD = 8 cm - KD = 6 cm

We can use the cosine rule to find the cosine of angle M and then calculate the angle M using the inverse cosine function.

Calculations

Using the cosine rule: KD^2 = MK^2 + MD^2 - 2 * MK * MD * cos(M)

Substituting the given values: 6^2 = 4^2 + 8^2 - 2 * 4 * 8 * cos(M)

Solving for cos(M): 36 = 16 + 64 - 64 * cos(M) 36 = 80 - 64 * cos(M) 64 * cos(M) = 80 - 36 64 * cos(M) = 44 cos(M) = 44 / 64 cos(M) = 0.6875

Now, to find the angle M: M = arccos(0.6875) M ≈ 45.57 degrees

Conclusion

The cosine of angle M in triangle MKD is approximately 0.6875, and the angle M itself is approximately 45.57 degrees.