Question

A pyramid with vertex V has a square base PQRS of side 8.5cm. If the slant face slopes at an angle of 60 degrees to the base, what is the correct height of the pyramid?

a) 7.37 cm
b) 10.0 cm
c) 14.7 cm
d) 4.25 cm

Answer 1

To find the height of the pyramid, we can use trigonometry and the given information about the slant face. The height of the pyramid is 7.37 cm.

Step-by-step explanation:

To find the height of the pyramid, we can use the trigonometric relationship between the slant height, the height, and the angle of the slant face. Let's denote the height of the pyramid as 'h'.

We can use the sine function to relate the slant height (8.5 cm), the angle (60 degrees), and the height (h): sin(60) = h / 8.5 cm.

Simplifying this equation, we get h = 8.5 cm * sin(60) = 7.37 cm. Therefore, the correct height of the pyramid is 7.37 cm (option a).