In δabc, m∠cab = 30°, m is the midpoint of
ab so that ab = 2·mc. find the angles of the triangle. find ab if bc = 7 ft. (preferably with a picture)

The angles of the ΔABC are:

AB= 14 ft

Step-by-step explanation:

Given:

A triangle ABC, with °

AB = 2MC

M is the mid-point of AB.

Let AB =

Therefore, AM = MB =

Also, MC =

∴ AM = MB = MC =

Now, consider triangle AMC,

∵ AM = MC

∴ °    ( )

Now, exterior angle BMC is given as the sum of opposite interior angles of triangle AMC.

Consider triangle BMC,

∵ MB = MC

∴

The sum of all interior angles is equal to 180°.

Therefore, °

Also, °

Therefore, the triangle ABC is a special right angled triangle with measures 30° - 60° - 90°.

For a special right angled triangle 30° - 60° - 90°, the hypotenuse is twice the base.

Here, AB is the hypotenuse and BC is the base. So,

Therefore, AB = 14 ft.

a - base

b - exponent

so,