An angle is in standard postion, such that sin  $\theta$θ = $\frac{-5}{7}$−57  . What are the possible values of  $\theta$θ , to the nearest degree, if 0 degrees $\le\theta<360$≤θ<360 degrees?

An angle is in standard postion, such that sin  $\theta$θ = $\frac{-5}{7}$−57  . What are the possible values of  $\theta$θ , to the nearest degree, if 0 $^{\circ}\le\theta<360^{\circ}$^?≤θ<360^? ?

Raphael tours the leaning tower of Pisa. From the base of the short side of the tower, Raphael walks 137m and measures the distance to the top of the short side of the tower to be 142 m, with angle of elevation of 23 degrees. Determine the height of the short side of the leaning tower of pisa.

The point (-9, 40) is on the terminal arm of an angle,  $\theta$θ in standard position. 

a. what is the length of the line segment connecting the orgin to the point (-9,40)

b. Determine the measure of  $\theta$θ , to the nearest tenth of a degree. 

Raphael tours the leaning tower of Pisa. From the base of the short side of the tower, Raphael walks 137m and measures the distance to the top of the short side of the tower to be 142 m, with angle of elevation of 23 degrees. Determine the height of the short side of the leaning tower of pisa. 

The point (-9, 40) is on the terminal arm of an angle,  $\theta$θ in standard position. 

a. what is the length of the line segment connecting the orgin to the point (-9,40)

b. Determine the measure of  $\theta$θ , to the nearest tenth of a degree. 

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.