Mathematics, 22.04.2020 04:26 estebanmff

A straight river flows east at a speed of 11 mi/h. A boater starts at the south shore of the river and wants to arrive at a point on the north shore of the river directly opposite the starting point. The motorboat has a speed of 22 mi/h relative to the water. In what direction should the boat be headed?

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The direction should the boat be headed is 60 degrees north 30 degrees west and this can be determined by using the trigonometric functions.

Given :

A straight river flows east at a speed of 11 mi/h. A boater starts at the south shore of the river and wants to arrive at a point on the north shore of the river directly opposite the starting point. The motorboat has a speed of 22 mi/h relative to the water.

The following steps can be used in order to determine the direction should the boat be headed:

Step 1 - The trigonometric function can be used in order to determine the direction should the boat be headed.

Step 2 - The mathematical expression of the cosine function is given by:

$\rm cos\theta=\dfrac{base}{hypotenuse}$

where $\theta$ is the direction should the boat be headed.

Step 3 - Now, substitute the known values in the above formula.

$\rm cos\theta=\dfrac{11}{22}$

Step 4 - Simplify the above expression.

$\rm cos\theta=\dfrac{1}{2}$

$\theta = 60^\circ$

Step 5 - So, the angle from the west axis is given by:

$90-60=30^\circ$

The direction should the boat be headed is 60 degrees north 30 degrees west.

For more information, refer to the link given below:

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Answer from: sullivanjakob

N 30 degree W

Step-by-step explanation:

We are given that

Speed of river flows=11 mi/h(East)

Speed of motorboat relative to water=22mi/h

We have to find the direction in which the boat should be headed.

Let direction of the boat = $\theta$

We know that

$Cos\theta=\frac{Base}{hypotenuse}$

Using the formula

$Cos\theta=\frac{11}{22}=\frac{1}{2}$

$Cos\theta=Cos60^{\circ}$

Because $Cos60^{\circ}=\frac{1}{2}$

$\theta=60^{\circ}$

Angle from the west axis= $90-60=30^{\circ}$ W

Hence, the direction of boat should be headed in N 30 degree W

Answer from: Quest

The question is kind of confusing. if it's asking how many variations of answers can you give. then do 4^5 for your answer.this would be something like the first question could be a and the 2nd c or first b next c etc. if you can, ask the teacher for a better confirmation of what it's asking. if i'm assuming correctly what it's asking, it's 625 different variations.

Answer from: Quest

Is a for each hour he works,his earnings go up by $4
This graph shows how much anthony earns babysitting, compared with the number of hours he works. sel

This graph shows how much anthony earns babysitting, compared with the number of hours he works. sel

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