Using the given information, the width of the river is 505.96 m
<h3>Bearing and Distances</h3>From the question, we are to determine the width of the river
Consider the given diagram,
Let F be the first position of the biker
S be the second position
and C be the position of the church
First, we will determine the distance covered from F to S
Speed = 160m/min
Time = 4 minutes
Using the formula,
Distance = Speed × Time
Distance covered = 160 × 4
Distance covered = 640 m
That is, /FS/ = 640 m
Now, consider ΔFSC
∠F = 90° - 70° = 20°
∠S = 90° + 56° = 146°
and ∠C = 180° - 20° - 146° = 14°
By the Law of Sines
∴
/FC/ = 1479.33 m
Now,
By SOH CAH TOA
NOTE: d is the width of the river
∴ d = /FC/ × cos70°
d = 1479.33 × cos70°
d = 505.96 m
Hence, the width of the river is 505.96 m
Learn more on Bearing and distances here: brainly.com/question/19351991
#SPJ1