Question

В треугольнике DEF известно, что DE = DF, EF = 16 tgF = 9/4. Найдите медиану DM этого треугольника

Answer 1

Дано: DE = DF 
          EF = 16
          tg∠F = 9/4
Найти: DM - ?

Решение

MD - медиана, тогда FM = EF / 2 =  16 / 2 = 8

По условию DE = DF, значит ΔFDE - равнобедренный,
тогда медиана MD - будет являться и высотой, тогда из прямоугольного треугольника FDM

tg∠F = DM / FM   отсюда

DM = tg∠F * FM = 9/4 * 8 = 18

Ответ: DM = 18

Answer 2

Triangle DEF

To find the length of the median DM in triangle DEF, we need to use the given information. Let's break down the information we have:

- DE = DF (the lengths of two sides of the triangle are equal) - EF = 16 - tgF = 9/4

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

DM = (1/2) * √(2 * DE^2 + 2 * EF^2 - DF^2)

Now let's substitute the given values into the formula:

DM = (1/2) * √(2 * DE^2 + 2 * EF^2 - DF^2)

Since DE = DF, we can simplify the formula:

DM = (1/2) * √(2 * DE^2 + 2 * EF^2 - DE^2)

DM = (1/2) * √(DE^2 + 2 * EF^2)

Now let's substitute the given values:

DM = (1/2) * √(DE^2 + 2 * EF^2)

DM = (1/2) * √(DE^2 + 2 * 16^2)

DM = (1/2) * √(DE^2 + 2 * 256)

To find the value of DE, we need more information. Unfortunately, the given information is incomplete and does not provide the necessary details to calculate the length of the median DM.