Answer:
The height of the triangular pyramid base is represented by s√3/2 units.
Step-by-step explanation:
This question focuses on calculating the height of the equilateral triangle at the base of the oblique pyramid.
According to the question, the equilateral triangle side has a length of a units.
Let’s review some properties of equilateral triangles:
a. All sides are identical in length, in this case, side s represents all sides.
b. All angles measure the same, at 60 degrees each.
c. Drawing a perpendicular line from the top vertex to the base divides the triangle into two right triangles, which have angles of 60 and 30 degrees, respectively.
To find the height of this triangular base, we can utilize either of the two right-angled triangles.
Recall the angles of 30, 60 and the side length s.
For height h calculation, trigonometric functions will assist us.
The relevant trigonometric relationship involves the sine of the angle (where side length s is the hypotenuse and height h is the opposite side relative to the 60-degree angle).
Thus, we can express this as:
Sine of an angle = opposite side length/hypotenuse length
sin 60 = h/s
Consequently, h = s sin 60.
In surd form, this yields:
sin 60 = √3/2.
Therefore, we find:
h = s * √3/2 = s√3/2 units.
