Marcos is flying a kite 35 feet above an oak tree. The angle of elevation to the top of the tree is 16 degrees and the angle of elevation to the kite is 25 degrees. What id the distance, b, to the nearest foot marcos is standing from the tree?

9514 1404 393

  195 ft

Step-by-step explanation:

The relationship between the horizontal distance, angle, and vertical height is given by ...

  Tan = Opposite/Adjacent

Referring to the attached diagram, we have ...

  tan(16°) = BT/MB

  tan(25°) = BK/MB

Solving for BT and BK, we can describe their difference as ...

  BT = MB·tan(16°)

  BK = MB·tan(25°)

  BK -BT = 35 = MB(tan(25°) -tan(16°))

Dividing by the coefficient of MB gives ...

  MB = 35/(tan(25°) -tan(16°)) = 35/0.179562

  MB = 195 . . . feet

Marcos is standing 195 feet from the base of the tree.

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

y=1/4x-4

step-by-step explanation: