Question

Please help The diagram below shows a square prism. The plane ABC is inside the

prism, and M is the midpoint of the base diagonal BC. MD. = square root 18
b Hence find, correct to the nearest degree, the angle that the plane ABC
makes with the base of the prism. Diagram is attached below.

Answer 1

43°

Explanation:

Triangle ADM is a right triangle with legs AD=4 cm and DM=√18 cm. The angle at M is the angle of interest. It can be found using the inverse tangent function.

Tan = Opposite/Adjacent

tan(∠AMD) = AD/MD = 4/√18

∠AMD = arctan(4/√18) ≈ 43.31°

The angle the plane makes is about 43°.

Answer 2

the measure of the angle that the plane ABC makes with the base of the prism = 43 degree (to the nearest degree)

Explanation:

We notice that the plane ABC and the base of the prism intersect along the line BC

And as the plane (ADM) is perpendicular to the line BC

then the angle between the plane ABC and the base of the prism is the angle AMD

Let θ be the measure of the angle AMD

`\begin{aligned}\tan (\theta) &=(A D)/(M D) \\&=(4)/(√(18))\end{aligned}`

`\begin{aligned}\Rightarrow \theta &=\tan ^(-1)\left((4)/(√(18))\right) \\&=43,31385 \ldots\end{aligned}`