Question

PQRST is a rectangular-based pyramid with a height of 9cm.

Find the angle between the line ST and the plane PQRS.
Give your answer correct to 1 decimal place.

Answer 1

54.1° (1 dp)

Explanation:

Let the center point of the rectangle PQRS = M

Calculate the length of the line SM using Pythagoras' Theorem:

a² + b² = c²

(11/2)² + (7/2)² = SM²

42.5 = SM²

SM = √42.5 cm

The height of the pyramid is 9 cm, therefore, MT = 9

Now we have a right angled triangle with base SM and height MT and hypotenuse ST

We want to find the angle TSM, so we can use the trig formula tan x = O/A, where x is the angle, O is MT and A is SM

tan TSM = MT/SM = 9/√42.5

TSM = arctan (9/√42.5) = 54.082088°

So the angle between the line ST and the plane PQRS = 54.1° (1 dp)