Instructions for finding a buried treasure includethe following: Go 736.4 paces at 130◦, turn to 199◦and walk 134 paces, then travel 157 paces at 195◦.

Question

Find the magnitude of the resultant displacement from the starting point.
Answer in units of paces.

What is the direction of the resultant displacement?
Use counterclockwise from due East as
the positive angular direction, between the limits of −180◦ and + 180◦.
Answer in units of degrees.

Answer 1

D = 736.4[130o] + 134[199o] + 157[195o].

X=736.4*Cos(130) + 134*Cos(199) + 157*Cos(195)
= -473.3 - 126.7 - 151.7 = -751.7 Paces.

Y=736.4*sin(130) + 134*sin(199) + 157*sin(195)
=564.1 - 43.63 - 40.63=479.8 Paces. Q2.

a. Magnitude=sqrt(X^2+Y^2) = 892 Paces.

b. Tan A = Y/X = 479.8/-751.7=-0.63833.
A = -32.6o = 32.6o N. of W. = 147.4o CCW
= The direction.