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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 c

yuradex [85]

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

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

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

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

/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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7 0

2 years ago

What is 1614 divided by 4

igor_vitrenko [27]

1614 divided by 4 is 403.5

7 0

3 years ago

Read 2 more answers

Over the last 3 evenings, Yolanda received a total of phone 96 calls at the call center. The third evening, she received 4 times

Ulleksa [173]

Yolanda received 17 calls on first day, 11 calls on second day and 68 calls on third day.

Step-by-step explanation:

Given,

Total calls received = 96

Let,

x be the number of calls received on second day.

Calls received on first day = x+6

Calls received on third day = 4(x+6)

Sum of calls received on three days = Total

$x+(x+6)+4(x+6)=96\\x+x+6+4x+24=96\\6x+30=96\\6x=96-30\\6x=66$

Dividing both sides by 6

$\frac{6x}{6}=\frac{66}{6}\\x=11$

Calls received on first day = x+6 = 11+6 = 17 calls

Calls received on second day = x = 11 calls

Calls received on third day = 4(11+6) = 4(17) = 68 calls

Yolanda received 17 calls on first day, 11 calls on second day and 68 calls on third day.

Keywords: addition, linear expression

Learn more about linear expressions at:

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7 0

3 years ago

Tom, Lisa, and Jane are competing in a cooking competition. They all used different amounts of sugar from a can containing 4 pou

Alika [10]

Answer:

im pretty sure its tom

Step-by-step explanation: because 13% as a decimal is 0.13, so compare that to the rest of the decimals.

4 0

3 years ago

Read 2 more answers

If a right triangle, the acute angles measure x+15 and 2x degrees. What is the measure of the smallest angle of the triangle?

saveliy_v [14]

Answer:

The measure of the smallest angle of the triangle is 40.

Step-by-step explanation:

A right triangle adds up to 180

x+15+2x+90=180

Combine like terms

3x+105=180

Subtract both sides by 105

3x+105=180

-105=-105

___________

3x=75 Divide by 3

x=25

Plug in 25 for x for equation expression

90=90

25+15=40

2(25)=50

Therefore for the smallest angle is 40

Hope this helps

6 0

3 years ago