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The base of a solid oblique pyramid is an equilateral triangle with an edge length of s units.
Which expression represents the height of the triangular base of the pyramid?

The base of a solid oblique pyramid is an equilateral triangle with an edge length of s units Which expression represents the height of the triangular base of t class=

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Answer:

Option B is correct.i.e.,

Step-by-step explanation:

Given: Pyramid with equilateral triangle as base

           Length of side of equilateral triangle = s unit

to find: height of equilateral triangle

Here we use a property of equilateral triangle.

Perpendicular from a vertex on a side and median of that side of a triangle is same in equilateral triangle.

All heights are of equal length. So, we just need to find one height or length of 1 altitude.

Figure of base triangle is attached

In Δ ABC

AB = BC = AC = s unit

AD is height

BD = [tex]\frac{BC}{2}\:=\:\frac{s}{2}\:units[/tex]

Now, In Δ ABD

using pythagoras theorem

BD² + AD² = AB²

[tex](\frac{s}{2})^2+AD^2=s^2[/tex]

[tex]\frac{s^2}{4}+AD^2=s^2[/tex]

[tex]AD^2=s^2-\frac{s^2}{4}[/tex]

[tex]AD^2=\frac{4s^2-s^2}{4}[/tex]

[tex]AD^2=\frac{3s^2}{4}[/tex]

[tex]AD=\sqrt{\frac{3s^2}{4}}[/tex]

[tex]AD=\frac{\sqrt{3}s}{2}[/tex]

[tex]AD=\frac{s}{2}\sqrt{3}[/tex]

Therefore, Option B is correct.i.e., [tex]\frac{s}{2}\sqrt{3}[/tex]

Ver imagen aquialaska

The expression (s√3)/2 represents the height of the triangular base of the pyramid option second is correct.

What is the triangle?

The triangle can be defined as a three-sided polygon in geometry and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

We have a solid oblique pyramid with a base of an equilateral triangle.

The base length of an equilateral triangle  = s units.

We know the height of a pyramid with an equilateral triangle divides the triangle base into two same parts.

So the half base length of an equilateral triangle = s/2 units

In an equilateral triangle, all the angles are the same with the measure of 60°

Now the height of the pyramid is given by:

[tex]\rm tan60 = \frac{h}{\frac{x}{\frac{s}{2} } }[/tex]        (in right angle triangle)

[tex]\rm h = tan60\times\frac{s}{2}[/tex]    (tan60° = √3)

[tex]h = \sqrt{3} \frac{s}{2} \\\\h= \frac{{s} }{2} \sqrt{3}[/tex]

Thus, the expression (s√3)/2 represents the height of the triangular base of the pyramid option second is correct.

Learn more about the triangle here:

brainly.com/question/25813512

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