https://file.aiquickdraw.com/mathbot/file/1729779576872ycj6vbeb.jpg

The problem is about a **right pyramid \(VABCD\)** with a square base, and you're asked to solve for:

(a) The **altitude** of the pyramid \(VX\).  
(b) The **length of \(AX\)**, where \(X\) is the intersection of the diagonals \(AC\) and \(BD\).  
(c) The **magnitude of angle \(VAX\)**.  

### Extracted Data:
- **AB** = 5 cm  
- **BC** = 3 cm  
- **VC** = 9 cm  

Let’s address each question step by step.

---

### Part (a): **Altitude of the pyramid \(VX\)**  
In a right pyramid, the altitude is the perpendicular distance from the apex \(V\) to the center of the base (point \(X\)).

Since \(X\) is the intersection of the diagonals \(AC\) and \(BD\) (center of the base), the diagonals bisect each other. So:
- The diagonals are the distances across the square or rectangular base.

To calculate \(VX\):
- If the base is a **rectangle** with sides \(AB = 5 \, \text{cm}\) and \(BC = 3 \, \text{cm}\), the center is:
\[
X = \left(\frac{5}{2}, \frac{3}{2}\right)
\]

So the diagonal across the base helps define the altitude. We'll calculate this next.

---

### Part (b) **Length of \(AX\)**  
(Point addtrsublok

VABCD is a right pyramid and X is the point of intersection of the diagonals AC and BD. Given that AB = 5 cm, BC = 3 cm, and VC = 9 cm. Evaluate: (a) the altitude of the pyramid VX (b) the length of AX (c) the magnitude of angle VAX.

Solve a right pyramid geometry problem involving a base with diagonals, calculating the altitude VX, the length AX, and the angle VAX. Given values include AB = 5 cm, BC = 3 cm, and VC = 9 cm. Step-by-step solutions for each part using Pythagoras' theorem and the cosine rule.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation