From a ship, the angle of elevation of a point, a, at the top of a cliff is 21°. after the ship has sailed 2,500 feet directly toward the foot of the cliff, the angle of elevation of ∠a is 47°. (assume the cliff is perpendicular to the ground.) the height of the cliff is __ feet.

10701.97 feet.

Step-by-step explanation:

Refer the attached figure

The angle of elevation of a point, A, at the top of a cliff is 21° i.e. ∠ACB = 21°

The ship has sailed 2,500 feet directly toward the foot of the cliff i.e. CD = 2500 feet.

Then the angle of elevation becomes 47° i.e.∠ADB = 47°

Let BD be x

So, BC = BD+DC=x+2500

Let the height of the cliff be h feet.

In ΔABD

We will use trigonometric ratios

   ---a

In ΔABC

We will use trigonometric ratios

  -----b

Equate a and b

Thus the height of the cliff is 10701.97 feet.

d

step-by-step explanation:

d

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: