An equilateral triangle has a radius of length 3 in. Find the length of an apothem

An equilateral triangle has a radius of length 3 in. Find the length of an apothem:

Here, radius 3 inch is the distance from center of the triangle to one vertex of the triangle.

Here is the diagram for the given.

Let’s take the right triangle to find Apothem. The right triangle has 30 degrees with vertex of the equilateral triangle. So, the right triangle is a special right triangle 30 60 90 degrees.

Let’s use special right triangle ratio or trigonometric ratio to solve for apothem.

Trigonometric way to find apothem:

For the right triangle and 30 degree angle, opposite side is Apothem and hypotenuse is 3.

So, let’s use sine ratio to solve.

Sin 30= Opposite side/Hypotenuse.

Sin 30 = Apothem/3

Multiply both sides by 3.

3 * sin 30 =Apothem

Find value of sin 30 using calculator in degree mode.

We get

3*0.5=Apothem.

1.5= Apothem

Answer: Apothem = 1.5in

In special right triangle way:

If we see we need to find the side opposite to 30 degree angle. So, it is half of hypotenuse.

So, short leg = 1/2 * hypotenuse

Short leg =1/2(3) =1.5 in.

Answer is 1.5 in.

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