Determine the value of  $\theta$θ, an angle in standard postion, where  $\sin\theta=-\frac{1}{2}$sinθ=−12  and tan $\theta=\frac{\sqrt{3}}{3}$θ=√33  ,  $0degrees\le\theta<360degrees$0degrees≤θ<360degrees.   

Troy has written a proof showing that the diagonals of a parallelogram are equal in length. The diagonals of a parallelogram are not necessarily equal so Troy must have made an error. Identify and explain his error.

Statement   |  Justification

AB = ED       |     Opposite sides of parallelogram

BAE = AED   |      Alternate interior angles

ABD = BDE   |     Alternate interoir angles

ABC = EDC   |   ASA

BC = EC      |   Corresponding sides of congruent angles

AC = DC      |   Corresponding sides of congruent angles

AE = BD      |   AC + CE = DC + CB

The use of a ladder is considered safe if the angle between the ground and the ladder is less than 75 degrees. Charlie's 5 ft long ladder is 1 ft from the base of a wall. 

a) Is the ladder being used safely?

b) How far away from the wall is the minimum distance charlie's other ladder should be if it is 10 ft long?

Explain why knowing a combination of four pairs of equal sides or equal angles guarantees one of the congruence relationships.

 $94.7°$9‍4.7° is the angle at the top

 In Alberta, ramps that are designed for people using mobility devices must meet certain safety requirments. One such requirment is that the angle between the ramp and the horizontal must be less than 4.8°. Explain whether or not the ramp below is acceptable. 

Determine the measrue of angle x in the diagram. Be sure to explain your reasoning.

how do you solve the following equation by completing the sqaure?

y= -x^2/90+4x/3