1. A​ blimp, suspended in the air at a height of 500 ​feet, lies directly over a line from a sports stadium to a planetarium. If the angle of depression from the blimp to the stadium is 31 degrees and from the blimp to the planetarium is 29 degrees ​, find the distance between the sports stadium and the planetarium. 2. Suppose you are headed toward a plateau 55 m high. If the angle of elevation to the top of the plateau is 60 degrees​, how far are you from the base of the​ plateau?

3. A radio transmission tower is 200 feet high. How long should a guy wire be if it is to be attached to the tower 19 feet from the top and is to make an angle of 45 degrees with the​ ground?
The guy wire should be ??? feet long.

19.side- angle- side

20. angle- side- angle

step-by-step explanation:

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

you can first factor out the n to get n(1+5). we know that 1+5 is 6, so we just have 6n.