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, so an equiangular triangle is an equilateral triangle.

The measures of the interior angle of an equilateral triangle is equal to 60 degrees

Applying the Pythagoras Theorem find out the height of triangle

$h^{2}=c^{2}-(\frac{c}{2})^{2}$

we have that

$c=6\ in$

substitute

$h^{2}=6^{2}-(\frac{6}{2})^{2}$

$h^{2}=36-9$

$h^{2}=27$

$h=\sqrt{27}=5.2\ in$

see the attached figure to better understand the problem

Answer 2

The height of the triangle is 5.2 inch.

Step-by-step explanation:

Given :

An equiangular triangle has one side of length six inches.

Solution :

An equiangular triangle is a triangle where all three interior angles are equal in measure, so an equiangular triangle is an equilateral triangle. The measures of the interior angle of an equilateral triangle is equal to $60^\circ$.

Now applying pythagorean theorem we get,

$h^2 = c^2-(\dfrac{c}{2})^2$

$h^2=\dfrac{3c^2}{4}$  ----- (1)

here c = 6 inch so from equation (1) we get,

$h = \sqrt{27}$

h = 5.2 inch

The height of the triangle is 5.2 inch.

For more information, refer the link given below

https://brainly.com/question/24252852?referrer=searchResults