Question

1. The prism-shaped roof has equilateral triangular bases. Create an equation that models the height of one of the roof's triangular bases in terms of its sides. In your final answer, include all necessary calculations.
I have a whole performance task on my page worth 100 points if anyone could help me please

Answer 1

Answer:

$h=\frac{\sqrt{3}}{2}b\ units$    

Step-by-step explanation:

we know that

An equilateral triangle has three equal sides and three equal interior angles (the measure of each interior angle is equal to 60 degrees)

see the attached figure to better understand tyhe problem

Let

h ----> the height of an equilateral triangle

b ---> the length side of an equilateral triangle

In the right triangle ABD

Applying the Pythagorean Theorem

$AB^2=AD^2+BD^2$

substitute the given values

$b^2=(\frac{b}{2})^2+h^2$  

$b^2=\frac{b^2}{4}+h^2$

$h^2=b^2-\frac{b^2}{4}$

$h^2=\frac{3}{4}b^2$

square root both sides

$h=\frac{\sqrt{3}}{2}b\ units$