Question

An equiangular triangle has one side of length six inches. What is the height of the triangle, drawn from that side, to the nearest tenth of an inch?

Answer 1

Answer:

The height of the triangle is 5.2 inches

Step-by-step explanation:

we know that

An equiangular triangle is a triangle where all three interior angles are equal in measure

Remember that an equilateral triangle has three equal sides and three equal interior angles

so

An equiangular triangle Is the same that an equilateral triangle. The measure of its interior angles is equal to 60 degrees

Let

h ----> the height of triangle

b ---> the length side of the triangle

Applying Pythagoras Theorem

$h^2=b^2-(b/2)^2$

we have

$b=6\ in$

substitute

$h^2=6^2-(6/2)^2$

$h^2=36-9$

$h^2=27$

$h=\sqrt{27}\ in$

$h=5.2\ in$

see the attached figure to better understand the problem