In this question , the triangle is equilateral triangle , with radius equals to 8 cm and we have to find the length of apotherm, a .
Using sine ratio rule,
[tex]sin C = \frac{ opposite}{hypotenuse}[/tex]
For triangle ODC, opposite is a cm and hypotenuse is of length 8 cm .
So we will get
[tex]sin 30 = \frac{a}{8}[/tex]
Multiplying both sides by 8
[tex]8 sin 30 =a \\ 8* \frac{1}{2} =a \\ a = 4 cm[/tex]
So the length of the apothem is 4 cm .
The measure of the apothem of an equilateral triangle is [tex]8\sqrt{3}[/tex].
Apothem refers to the perpendicular to the right side of the triangle which creates the right angle.
Given
An equilateral triangle with a radius of 8 cm.
Let, the apothem of an equilateral triangle be x.
In the triangle the measure of the cos angle is;
[tex]\rm Cos30=\dfrac{base}{hypotenuse}\\\\\dfrac{\sqrt{3} }{2}=\dfrac{\dfrac{x}{2}}{8}\\\\\dfrac{\sqrt{3} }{2}=\dfrac{x}{2}\times \dfrac{1}{8}\\\\\dfrac{\sqrt{3} }{2}=\dfrac{x}{16}\\\\2x=16\sqrt{3}\\\\x=\dfrac{16\sqrt{3}}{2}\\\\x=8\sqrt{3}}[/tex]
Hence, the measure of the apothem of an equilateral triangle is [tex]8\sqrt{3}[/tex].
To know more about equilateral triangles click the link given below.
https://brainly.com/question/4268382
