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Messages in bottles have been used to send distress messages, in crowdsourced scientific studies of ocean currents, as memorial tributes, to send deceased loved ones' ashes on a final journey, to convey expedition reports, and to carry letters or reports from those believing themselves to be doomed. Invitations to prospective pen pals and letters to actual or imagined love interests have also been sent as messages in bottles.

The lore surrounding messages in bottles has often been of a romantic or poetic nature.

Use of the term "message in a bottle" has expanded to include metaphorical uses or uses beyond its traditional meaning as bottled messages released into oceans. The term has been applied to plaques on craft launched into outer space, interstellar radio messages, stationary time capsules, balloon mail, and containers storing medical information for use by emergency medical personnel.

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).