Question

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? Five-halves StartRoot 2 EndRootunits Five-halves StartRoot 3 EndRootunits 5 StartRoot 2 EndRootunits 5 StartRoot 3 EndRootunits

Answer 1

Answer:

The height of the triangular base of the pyramid is s√3/2 units

Step-by-step explanation:

Here in this question, what we are concerned with is to calculate the height of the equilateral-triangle base of the oblique pyramid.

From the question, we are told that the equilateral triangle has a length of a units.

Let’s have a recall on some of the properties of equilateral triangles;

a. All sides are of equal lengths. Meaning side s is the length of all the sides in this case.

b. All angles are equal, meaning they are 60 degree each.

c. Dropping a perpendicular line from the top vertex to the base length will split the equilateral triangle into two right-angled triangles of angles 60 and 30 each.

So to find the height of this triangular base, we can use any of the two right angled triangles.

Kindly recall that the properties of each would be angles 30, 60 and side length s

so to calculate the height h, we can use trigonometric identities

Mathematically, the trigonometric identity we can use is the sine( side length s represents the hypotenuse, while the height h represents the opposite facing the angle 60 degrees)

Thus; we have

Sine of an angle = length of the opposite/length of hypotenuse

sin 60 = h/s

h = s sin 60

In surd form,

sin 60 = √3/2

Thus;

h = s * √3/2 = s√3/2 units