Question

In △ABC, m∠CAB=30° and M is the midpoint of AB so that AB=2CM. Find the angles of the triangle. Find AB if BC=7 ft.

Answer 1

angle ACB = 90 degrees

angle B = 60 degrees

AB = 14ft.

Answer 2

hypotenuse side AB is twice than BC, i.e. 14 ft.

Explanation:

Given data:

angle CAB = 30 degree

M is mid point of AB and AB = 2 times of CM

We can say that, |MA| = |MB| = |MC|. and point A, B, and C are equidistant from M. It signifies that the point M is act as center of the circle which circumscribed around the given triangle ABC.

Therefore AB is diameter of circle and angle ACB is leaning on diameter AB.

It signifies that the angle ACB is 90 degree angle and the triangle ABC is right-angled triangle.

Since the angle CAB is 30 degree, therefore the other acute angle is 90-30 = 60 degree.

Thus the triangle ABC is (30 - 60 - 90) degree triangle.

Since side BC opposite to 30 degree is given as 7 ft, therefore hypotenuse side AB is twice than BC, i.e. 14 ft.