Question

the base of a solid oblique pyramid is an equilateral triangle with a base edge length of 14 units. what is bc, the height of the pyramid? 7 units 7√2 units 14 units 14√2 units

Explanation:

Step1: Identify base triangle property

The base is an equilateral triangle with side length 14, so the distance from A to the projection of D on AC (the midpoint-related horizontal segment) is the length of the base edge, which is 14 units. This is the adjacent side to the 45° angle in right triangle ABC.

Step2: Use trigonometry for height

In right triangle \(ABC\), \(\tan(45^\circ) = \frac{BC}{AC}\). We know \(\tan(45^\circ)=1\) and \(AC = 14\) units.
\(1 = \frac{BC}{14}\)

Step3: Solve for BC

Rearrange the equation to isolate \(BC\):
\(BC = 14 \times 1 = 14\)

Answer:

14 units