Question #63017

1 Answer
Jul 17, 2017

Answer:

#"distance" = 54.6# #"m"#

Explanation:

We're asked to find how far Sam's head is from the helicopter, with some given measurements.

The helicopter is supposedly traveling vertically upward, and its position after #10# #"s"# going at a constant speed of #5# #"m/s"# is

#(5"m"/(cancel("s")))(10cancel("s")) = 50# #"m"#

The angle of elevation from Sam to the helicopter at this time is given as #62^"o"#. (I'll assume this angle is taken from his head height.)

We also know Sam's height is #1.8# #"m"#, so the vertical distance from Sam's head to the helicopter is

#50# #"m"# #- 1.8# #"m"# #= 48.2# #"m"#

Using trigonometry, we can find the hypotenuse of the right triangle created in this problem:

#sin(62^"o") = (48.2color(white)(l)"m")/x#

#x = (48.2color(white)(l)"m")/(sin(62^"o")) = color(red)(54.6# #color(red)("m"#