Respuesta :
Since the angle is isosceles, angle A and angle B have the same measure,
The sum of the angles of any triangle is 180°.
So 2 times the measure of angle B plus 120° = 180°, then the equation:
[tex]2x+120=180[/tex]
Solving for x we get: [tex]x=30[/tex]
Now we use the law of sine on the triangle BMC like this:
[tex] \frac{12}{\sin30} = \frac{BC}{\sin 60} [/tex]
Solving for BC we get : [tex]BC=20.7[/tex]
We apply the law of sin again on the isosceles triangle ABC like this:
[tex] \frac{AB}{\sin 120} = \frac{20.7}{\sin 30} [/tex]
Solving for AB we get:
[tex]AB=36[/tex]
The sum of the angles of any triangle is 180°.
So 2 times the measure of angle B plus 120° = 180°, then the equation:
[tex]2x+120=180[/tex]
Solving for x we get: [tex]x=30[/tex]
Now we use the law of sine on the triangle BMC like this:
[tex] \frac{12}{\sin30} = \frac{BC}{\sin 60} [/tex]
Solving for BC we get : [tex]BC=20.7[/tex]
We apply the law of sin again on the isosceles triangle ABC like this:
[tex] \frac{AB}{\sin 120} = \frac{20.7}{\sin 30} [/tex]
Solving for AB we get:
[tex]AB=36[/tex]
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
