Hello, john edgar!
Did you make a sketch?
I'll explain the first one. (The second one is exactly the same.)
The bearing from Winston-Salem to Danville is N 42° E.
The bearing from Danville to Goldsboro is S 48° E.
Mark, driving at 60mph, takes one hour to go from Winston-Salem to Danville
and 1.8 hour to go from Danville to Goldsboro.
Find the distance from Winston-Salem to Goldsboro. Code:
N D
: *
: * : *
: 60 *42°:48°*
: * : *
:42°* : * 108
: * : *
W * : *
: * : *
: : * *
: : * *
: S * G
"The bearing from Winston-Salem to Danville is N 42° E."
. . / NWD = 42° . . . hence: / WDS = 42°.
"The bearing from Danville to Goldsboro is S 48° E."
. . / SDG = 48°.
"Mark, driving at 60mph, takes one hour to go from Winston-Salem to Danville"
. . WD = 60
"and 1.8 hour to go from Danville to Goldsboro."
. . DG = 108
Note that: ./ D .= .42° + 48° .= .90°
. . ∆ WDG is a right triangle!
Use the Pythagorean Theorem to determine WG.