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grin007 [14]
3 years ago
5

The height of a radio tower is 400 ​feet, and the ground on one side of the tower slopes upward at an angle of 10degrees. ​(a) H

ow long should a guy wire be if it is to connect to the top of the tower and be secured at a point on the sloped side 190 feet from the base of the​ tower? ​(b) How long should a second guy wire be if it is to connect to the middle of the tower and be secured at a point 190 feet from the base on the flat​ side?

Mathematics
1 answer:
Anettt [7]3 years ago
4 0

Answer:

  (a)  412 ft

  (b)  276 ft

Step-by-step explanation:

Consider the attached diagram.

(a) The internal angle of triangle RBT at B is 90° -10° = 80°. Since we know lengths RB and BT, we can find the length RT using the law of cosines:

  RT² = RB² +BT² -2·RB·BT·cos(80°) = 190² +400² -2·190·400·cos(80°)

  RT² ≈ 169,705.477

  RT ≈ √169,705.477 ≈ 411.95

The guy wire to the hillside should be about 412 feet long.

__

(b) The Pythagorean theorem can be used to find the shorter wire length.

  LM² = LB² +MB²

  LM = √(190² +200²) = √76,100

  LM ≈ 275.86

The guy wire to the flat side should be about 276 feet long.

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postnew [5]

Answer:

Union and Intersection

Step-by-step explanation:

We know that the algebra of sets define the properties and laws of the sets.

The basic operations of sets are,

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Since, the operations addition, subtraction, multiplication and division are the basic arithmetic operations of numbers.

i.e. they are not in the algebra of sets.

So, we get that out of the given options, the operations in algebra of sets are Union and Intersection.

7 0
3 years ago
Plz answer!! thanks
jeka94

Answer:

x = 10

y = 40

Step-by-step explanation:

60° + (2x + 7y)° = 180° because these two angles are supplementary

So 2x + y would be equal to 60°

60° + (2x + 7y)° = 180° subtract 60 from both sides

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2x + 7y -2x - y = 120 - 60 -2x will eliminate 2x

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if 2x + y = 60 the we need to replace x with the value we found

2×10 + y = 60

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4 0
2 years ago
Scott earned 20 points more on his most recent math test than he earned on the previous test. If he earned at least 80 points on
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Answer:

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If Scott earned 20 points more on this test, then he earned 20 points less on the last test. 20 points less than "at least 80" is "at least 60."

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sergij07 [2.7K]

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