Question

Help w/ Trig Questions? #2

Hi, here are just two questions. I know you like to answer them as separate but there are way too many. Please show your work and make a picture to help!

Answer 1

`Angle ADM = cos^-1(1/(2sqrt2))`
`ACD=180/3=60^@`

Explanation:

Given:
All the sides in the square based pyramid is `20`cm
In the diagram,
BED is a triangle right angled at B
By pythagoras theorem
`BD^2=BE^2+ED^2`

`sqrt(20^2+20^2)=sqrt800`
`BD=1/2sqrt800=sqrt200`

M, being the midpoint of the diagonal BD
`BM=DM=1/2(BD)=1/2sqrt200=sqrt50=5sqrt2`

In the right angled triangle, DMA, right angled at M
adjacent side `DM=5sqrt2`
hypotenuse`DA=20`

`cosADM=(adj)/(hyp)=(5sqrt2)/20sqrt2/4=1/(2sqrt2)`
implies

`Angle ADM = cos^-1(1/(2sqrt2))`

Since the sides AD, AC, CD are equal, they form an equilateral angle.
All the angles are equal

Hence,
`ACD=180/3=60^@`