Question

You are riding along a straight river from east to the west at speed of 160m/m. At a given time, you will see the bearing of a church on the other parallel road is N 70 degrees W, and 4 minutes later the bearing is N 56 degrees W. What is the width of the river? (Round your answer to two decimal points)

Answer 1

Using the given information, the width of the river is 505.96 m

Bearing and Distances

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

$\frac{/FC/}{sin\ S}= \frac{/FS/}{sin\ C}$

∴ $\frac{/FC/}{sin\ 146^\circ}= \frac{640}{sin\ 14^\circ}$

$/FC/ =\frac{640 \times sin \ 146^\circ}{sin \ 14^\circ}$

/FC/ = 1479.33 m

Now,

By SOH CAH TOA

$cos \ 70^\circ = \frac{d}{/FC/}$

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

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