Question 1205998: I was able to do most part of this assignment by myself but I have no idea of for the last question:
A plane is flying west at 200 mph. The wind begins blowing S30°W at 25 mph.
1. What is the ground speed of the plane now? (nearest tenth)
R = 213.6
2. When you solve the triangle, what is the smallest angle? (nearest hundredth)
sin(120) / 213.6 = sin(θ) / 25
sin(θ) = sin(120) x 25 / 213.6
θ = arcsin(sin(120) x 25 / 213.6)
θ = 5.45degrees
3. What is the largest angle of the triangle?
120degrees
4. What is the remaining angle? (nearest hundredth)
y = 54.55degrees
5. What is the direction of the plane's new path? (The answer will be written using compass points such as N17°W.)
This is the question that I dont know how to answer
Found 3 solutions by josgarithmetic, math_tutor2020, ikleyn:
Answer by josgarithmetic(39630)   (Show Source):
Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!
Refer to the diagram made at this link
https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.1205915.html
(credit goes to tutor Edwin McCravy)
The plane wants to fly directly west along the longer blue vector.
The wind pushes the plane along the diagonal blue vector such that the plane's actual path is along the red vector.
It's like a game of tug-of-war.
Let's label the points of the triangle A,B,C where I'll start in the top left corner and work clockwise.
The plane starts at B. It wants to move to A. Instead the wind pushes it to C.
If we let D represent a point directly south of point A, then angle CAD is the S30°W angle mentioned.
It's where you look directly south and then turn 30° westward.
Add on 90 degrees (the measure of angle DAB) to determine the measure of angle CAB.
So,
angle CAB = angleCAD+angleDAB = 30+90 = 120
In short,
Angle CAB = 120°
Use the law of cosines as tutor Edwin mentions to determine that  approximately.
This rounds to 213.6 mph.
This is the groundspeed along the red vector. The original speed (200 mph) has been increased to roughly 213.6 mph due to the wind pushing it slightly.
Then we use the law of sines to find the smallest angle.
The smallest angle is opposite the smallest side (AC = 25)
sin(A)/a = sin(B)/b
sin(120)/213.60009 = sin(B)/25
sin(B) = 25*sin(120)/213.60009
sin(B) = 0.10136
B = arcsin(0.10136)
B = 5.81749
B = 5.82
The smallest angle is roughly 5.82° which is opposite side AC = 25.
This is the approximate measure of angle ABC. The angle complementary to this is 90-5.82 = 84.18°
If we let point E be directly south of B, then angle EBC = 84.18°
The plane is traveling along the red vector in the direction of S84.18°W
Place yourself at point B, face directly south, and then rotate roughly 84.18° westward so that you're aiming for point C.
The largest angle is 120° we found earlier (angle CAB).
The remaining angle is 180-120-5.82 = 54.18° approximately.
This is angle ACB.
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Summary:- R = 213.6
- smallest angle = 5.82°
- largest angle = 120°
- remaining angle = 54.18°
- direction of the plane's new path = S84.18°W
Answer by ikleyn(52898)  (Show Source):
You can put this solution on YOUR website! .
You incorrectly determined the angle 5.45 degrees.
Its true value is 5.82 degrees (approximately).
As soon as you determined two angles of a triangle, the third angle of the
triangle is 180 degrees minus the sum of the two found angle measures.
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