Question

Треугольнике MNK: MN = NK = 16 см, ∠K = 72°. Найди медиану ME, округлив его до целого числа.​

Answer 1

Ответ:

11см

Объяснение:

Answer 2

Task: Finding the median of triangle MNK

To find the median of triangle MNK, we need to know the lengths of the sides MN and NK, as well as the measure of angle K.

Given: - MN = NK = 16 cm - ∠K = 72°

To find the median ME, we can use the formula for the length of a median in a triangle:

ME = (1/2) * √(2 * (MN^2 + NK^2) - MK^2)

Let's substitute the given values into the formula and calculate the median.

Step 1: Calculate MK using the Law of Cosines: MK^2 = MN^2 + NK^2 - 2 * MN * NK * cos(∠K)

Step 2: Substitute the values into the formula for the median: ME = (1/2) * √(2 * (MN^2 + NK^2) - MK^2)

Now let's calculate the median ME.

Step 1: Calculate MK: MK^2 = 16^2 + 16^2 - 2 * 16 * 16 * cos(72°) MK^2 = 256 + 256 - 512 * cos(72°) MK^2 = 512 - 512 * cos(72°)

Step 2: Calculate ME: ME = (1/2) * √(2 * (16^2 + 16^2) - MK^2) ME = (1/2) * √(2 * (256 + 256) - (512 - 512 * cos(72°))) ME = (1/2) * √(2 * 512 - (512 - 512 * cos(72°))) ME = (1/2) * √(1024 - 512 + 512 * cos(72°)) ME = (1/2) * √(512 + 512 * cos(72°))

Now we can calculate the value of the median ME.

Using a calculator, we find that ME ≈ 3705 (rounded to the nearest whole number).

Therefore, the median ME of triangle MNK, rounded to the nearest whole number, is 3705 cm.

Please let me know if there's anything else I can help you with!