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A weather balloon is 529 meters above the ground. Two weather stations, A and B, monitor the balloon’s progress. Compare the measures of the different angles of elevation and depression that are labeled in the diagram. Which statements are true? Check all that apply. x > y v > x w = y y < v v = w x < w

A weather balloon is 529 meters above the ground Two weather stations A and B monitor the balloons progress Compare the measures of the different angles of elev class=

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frika

Answer:

Correct choices are A, C and D

Step-by-step explanation:

Consider two right triangles:

  • first with legs h=529 m and 229 m;
  • second with legs h=529 m and 347 m.

Then

[tex]\tan x=\dfrac{529}{229},\\ \\\tan y= \dfrac{529}{347}.[/tex]

Since

[tex]\dfrac{529}{229}> \dfrac{529}{347},[/tex]

then [tex]\tan x>\tan y\Rightarrow x>y[/tex] (option A is true).

You are given two parallel lines. Angles x and v and y and w are alternate interior angles, then x=v, y=w. This means that option B is false and option C is true. Option D is also true, because

[tex]x>y \text{ and } x=v \text{ gives that } v>y[/tex]

and option E is false, because

[tex]x>y \text{ and } y=w \text{ gives that } x>w.[/tex]

onyebuchinnaji

The true statements from the size of the angles of the given triangle are [tex]x>y, \ v= x, \ \ w = y, \ \ y <v , \ \ x >w[/tex].

The given parameters;

  • Height of the balloon, h = 529 m
  • Length of first half of AB = 229 m
  • Length of second half AB = 347 m

The length of A to the balloon point is calculated as follows;

[tex]AT^2= 529^2 + 229^2\\\\AT = \sqrt{529^2 + 229^2} \\\\AT = 576.4 \ m[/tex]

The length of B to the balloon point is calculated as follows;

[tex]BT^2 = 347^2 + 529^2\\\\BT = \sqrt{347^2 + 529^2} \\\\BT = 632.7 \ m[/tex]

The size of the interior angles of the triangle depends on the size of the length opposite the angle.

  • The largest angle is x opposite to 632.7 m
  • The second largest angle is y opposite to 576.4 m

For exterior angles;

  • v = x (alternate angles
  • w = y (alternate angles)

Thus, we can conclude that the true statements from the size of the angles of the given triangle are [tex]x>y, \ v= x, \ \ w = y, \ \ y <v , \ \ x >w[/tex].

Learn more here:https://brainly.com/question/19691610

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