Respuesta :
Answer:
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 =[tex]\theta[/tex]
We know that
[tex]Cos\theta=\frac{Base}{hypotenuse}[/tex]
Using the formula
[tex]Cos\theta=\frac{11}{22}=\frac{1}{2}[/tex]
[tex]Cos\theta=Cos60^{\circ}[/tex]
Because [tex]Cos60^{\circ}=\frac{1}{2}[/tex]
[tex]\theta=60^{\circ}[/tex]
Angle from the west axis=[tex]90-60=30^{\circ}[/tex]W
Hence, the direction of boat should be headed in N 30 degree W
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:
[tex]\rm cos\theta=\dfrac{base}{hypotenuse}[/tex]
where [tex]\theta[/tex] is the direction should the boat be headed.
Step 3 - Now, substitute the known values in the above formula.
[tex]\rm cos\theta=\dfrac{11}{22}[/tex]
Step 4 - Simplify the above expression.
[tex]\rm cos\theta=\dfrac{1}{2}[/tex]
[tex]\theta = 60^\circ[/tex]
Step 5 - So, the angle from the west axis is given by:
[tex]90-60=30^\circ[/tex]
The direction should the boat be headed is 60 degrees north 30 degrees west.
For more information, refer to the link given below:
https://brainly.com/question/11709244
