Precalculus question 6. find the value of x. round to the nearest degree a. 33 degrees b.40 degrees c.50 degrees d.57 degrees 7. a slide 5.1m long makes an angle of 35 degrees with the ground. to the nearest tenth of water, how far above the ground is the top of the slide? a. 3.6 m b. 2.9 m c. 4.2 m d. 7.3 m 23. explain how to find the reference angle for 1,406 degrees. find the rectangle angle.

Some information is missing for #6.
#7: use sine, sin35=h/5.1, h=5.1*sin35, use a calculator, h≈2.9
#23: to find the reference angle, keep subtracting the number by 360, until the remaining difference is the smallest positive number.
1406-360-360-360=326. the reference angle is 326.
now look at the remainder, the terminal line of 326 degree is in the 4th quadrant between 270 and 360, the the reference angle is 360-326=34, the angle between the terminal line and the positive x axis. 34 is the answer.

A rectangle is a quadrilateral with either two opposite sides equal and parallel to each other. That is AB is parallel and equal to CD and AD parallel and equal to BC. Parallel lines have equal slopes.
Thus, AB slope is 2, while that of CD is also 2, therefore they are parallel to each other. In addition the modulus of AB and that of CD is the same thus they are equal in length.
AD slope is -1/2 while that of BC is also -1/2 therefore the two are parallel to each other. In addition they are equal in length therefore they are equal in length. 
Moreover AB is perpendicular to BC and AD (product of slope of two perpendicular lines is -1)
Therefore, it can be concluded that Quadrilateral ABCD is a rectangle.