Question

A cuboid abcdefgh is shown bc=6.8cm de=9.3cm angle bac=52 find the size of the angle between CF and the plane ABCD GIVE YOUR ANSWER CORRECT TO 1 DECIMAL PLACE

Answer 1

Answer:

43 degrees

Step-by-step explanation:

DE is the diagonal of rectangle AEDH

CF is the diagonal of the opposite rectangle BFGC

Since opposite diagonals of a cuboid are equal, we therefore have that:

CF=DE=9.3cm

Also,

BC=6.8cm

In Triangle BFC, Angle B =90 degrees, therefore Triangle BFC is a right triangle.

We are required to determine the angle between CF and the plane ABCD.

This is Angle BCF in Right Triangle BFC.

Using Trigonometry

$\cos \theta = \dfrac{6.8}{9.3}\\\theta=\arccos \dfrac{6.8}{9.3}\\\theta=43.0^\circ$

Therefore:

Angle BCF=43 degrees.

The angle between CF and the plane ABCD is 43 degrees.