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) How 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?

  (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.

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(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.

just needed some points but try socratic

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!