A ramp makes an acute angle with respect to the horizontal. Any two points along either edge of the ramp that are 12 feet apart differ in their horizontal positions by 11.5 feet. Give the value of in degrees. Round your answer to four decimal places

43.7811 feet

Step-by-step explanation:

Hi, since the situation forms a right triangle (see attachment) we have to apply the next trigonometric function.  

Tan α = opposite side / adjacent side  

Where α is the acute angle with respect to the horizontal (x), the opposite side is the height of the ramp, and the adjacent side is the horizontal distance between the ramp edges.

Replacing with the values given:  

Tan x = 11.5/ 12

Solving for x  

x = arc tan (11.5/12)

x = 43.7811 feet

Feel free to ask for more if needed or if you did not understand something.  

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hope this .. : d

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.