Two bicyclists, starting at the same place, are riding toward the same campgroun
ID: 1619888 • Letter: T
Question
Two bicyclists, starting at the same place, are riding toward the same campground by different routes. One cyclist rides 1170 m due east and then turns due north and travels another 1510 m before reaching the campground. The second cyclist starts out by heading due north for 1910 m and then turns and heads directly toward the campground. (a) At the turning point, how far is the second cyclist from the campground? (b) In what direction (measured relative to due east within the range (-180 degree, 180 degree]) must the second cyclist head during the last part of the trip?Explanation / Answer
(a)
The two sides of the triangle have lenghts of 1910 m - 1520 m = 400m
from the pythagorean theorem
d= sqrt ( 1170)^2 + 400^2 = 1236.48 m
(b)
since the lenghts of the sides opposte and adjacent to the angle theta are known
tan theta = ( 400/1170)
theta = tan^-1 ( 400/1170)
=18.87 degree south of east