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gmany

Look at the picture.

This is isosceles triangle. Therefore, the angles at the base are congruent.

m∠ BAC = m∠ABC.

We know, the sum of the measures of the angles in a triangle is equal 180°.

Therefore:

m∠BAC + m∠ABC + m∠ACB = 180°

2m∠ABC + 120° = 180°     subtract 120° from both sides

2m∠ABC = 60°     divide both sides by 2

m∠ABC = 30°

m∠MCB = 90° → ΔMCB is a right triangle (30 - 60 - 90).

The sides of that triangle are in proportion: 1 : √3 : 2.

Therefore MC : BC : MB = 1 : √3 : 2

MC = 12 → BC = 12√3 and MB = 2 · 12 = 24

ΔCDB is the right triangle (30 - 60 - 90) too.

Therefore CD : BD : BC = 1 : √3 : 2

CD = 1/2 BC → CD = 1/2(12√3) = 6√3

BD = CD√3 → BD = 6√3(√3) = 6(3) = 18

AB = 2BD therefore your answer is:

AB = 2(18) = 36


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AB length is 24 cm

Further Explanation

The first step, find the length of BM

Given length CM = 12 cm

and length CB = 12 sqrt 3

sin 60 ° = CB / BM

1/2 sqrt 3 = 12 sqrt 3 / BM

BM = 1/2 sqrt 3 * 12 sqrt 3

BM = 18 cm

Then find the length of the MA

sin 30 ° = CM / MA

1/2 = 12 / MA

MA = 1/2 * 12

MA = 6 cm

So, the length of AB is BM + MA = 18 cm + 6 cm = 24 cm

A triangle is the name of a shape made from three sides in the form of a straight line and three angles. The mathematician Euclid who lived around 300 BC found that the sum of the three angles on a triangle on a flat plane was 180° degrees. This allows us to calculate the magnitude of one angle when the other two angles are known.

Classification of triangles

According to the length of the sides:

  • The equilateral triangle is a triangle whose sides are the same length. As a result, all angles are equal, which is 60 °.
  • Isosceles triangle is a triangle whose two sides are the same length. This triangle has two equal angles.
  • An arbitrary triangle is a triangle whose sides have different lengths. Big all the angles are also different.

According to the biggest angle:

  • A right triangle is a triangle whose angle is equal to 90°. The side in front of the 90° angle is called the hypotenuse or the hypotenuse.
  • An acute triangle is a large triangle, all angles <90°
  • An obtuse triangle is a large triangle with an angle of> 90°

Learn More

Triangle Formula https://brainly.com/question/11585941

Find a length from part triangle https://brainly.com/question/11740962

Details

Class: Middle/High School and College

Subject: Mathematics

Keyword: degrees, angles, triangle

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