A communications tower is located at the top of a steep hill, as shown. The angle of inclination of the hill is 58°. A guy wire is to be attached to the top of the tower and to the ground, 200 m downhill from the base of the tower. The angle in the figure is determined to be 10°. Find the length of cable required for the guy wire. (Round your answer to the nearest meter.)

Trent wants to buy 2 packs of trading cards for 3 dollars each. the trading card packs that trent normally buys tend to come in packs of 6, 10, 12, or 15 cards. after selecting 2 packs, trent found that the first pack of cards cost 25 cents per card, and the second pack cost 30 cents per card. trent uses this information to write the equations below in order to compare c, the number of cards in each pack.

If tan2a=cot(a+60), find the value of a, where 2a is an acute angle

Events a and b are independent. the probability of a occurring is 2/5. the probability of b occurring is 1/4. what is p(a and b)?