Respuesta :

ISALE
From the equilateral (60-60-60) triangle with all legs of length 1, we can view half the triangle, forming a 30-60-90 triangle, with the hypotenuse measuring 1, the short leg1/2, and the long leg 3 2. Therefore, we have sin 30° = 1/2, cos 30° = 3 2, sin 60° = 3 2 and cos 60° = 1/2.

i hope this help

The exact value of sin 30° is 1/2 as the simplified fraction form and 0.5 in the desimal form.

What is an equilateral triangle?

An equilateral triangle is the triangle in which all the three sides are of equal length in measure.

Let suppose a equillateral triangle ABC. In this triangle each angle will be equal to the 60 degree measure.

[tex]m\angle A=60\\m\angle B=60\\m\angle C=60[/tex]

Now draw a perpendicular AD from point A on BC. This will divide the BC is two equal parts as,

[tex]BC=\dfrac{1}{2}BD=\dfrac{1}{2}CD[/tex]

The angle A divides in two parts and the measure of angle [tex]\angle BAD[/tex] be equal to 30 degrees.  The value of BD will be equal to the half of the AB.

[tex]2BD=AB[/tex]

Now in traingle ADB the value of sin 30 degree is equal to the ratio of opposite side BD and hypontenuse side AB. Thus,

[tex]\sin30^o=\dfrac{BD}{AB}\\\sin30^o=\dfrac{BD}{2BD}\\\sin30^o=\dfrac{1}{2}\\\sin30^o=0.5[/tex]

Hence, the exact value of sin 30° is 1/2 as the simplified fraction form and 0.5 in the desimal form.

Learn more about the equilateral triangle here;

https://brainly.com/question/1099318