Find graphically the tensions in the cables

An object of weight 20kN is supported from above by two cables inclined at 40 and 70 degrees to the horizontal as shown (please see attachment)

SOLVE ANALYTICALLY STATIC FORCE SYSTEMS INVOLVING NO MORE THAN 3 CO PLANAR FORCES

Please see the attached file for full problem description.

Proving identities

Provide reasons (identities, operations, etc.) for each step in the proof. Include any thoughts, ideas or strategies used to prove the identity.

Distance Problem

I need help finding a formula that can be used to solve the following problem: A Man walking his dog along a straight country road spots a friend one mile away. His dog sprints ahead to greet her. When the dog reaches her it turns back to the man. when it reaches him it sprints back to the woman. The process continues until the two people meet. If each person walks at 2 MPH and the dog runs at 8 mph, how far does the dog run before the two people meet?

Verify the identities, show all work

Verify the following identities, show all work secx(1-sin^2x)=cosx tanx + cotx=secxcscx cotx/cosx=cscx csc^2x(1-cos^2x)=1 cosxcotx + sinx=cscx