A plane is heading west at 200 mph. The wind is blowing S30°W at 25 mph.
1. What is the ground speed of the plane?
2. When you solve the triangle, what is the smallest angle?
3. What is the largest angle of the triangle?
4. What is the remaining angle?
5. What is the bearing of the plane?
Please help, I been on this for TWO MONTHS* and my teacher won't help me out. (I'm home-schooled.)
This is a routine question, and would be an introductory type of question in a course of vector geometry.
The fact that " I been on this for TWO MONTHS* " (your grammar also needs improvement) illustrates my objection to "home schooling"
..... end of editorial...
I have a triangle with sides of 200 and 25 with a contained angle of 120°
let the side opposite your 120° angle be x
by the cosine law ....
x^2 = 200^2 + 25^2 - 2(200)(25)cos120°
...
x = 213.6
so the ground speed of the plane is 213.6 mph
The smallest angle would be opposite the 25 side, by sine law
sinØ/25 = sin120/213.6
sinØ = .10136..
Ø = 5.8
largest angle is 120°
smallerst is 5.8°
third angle is 54.2°
bearing of plane is W 5.8° S
1. The ground speed of the plane can be calculated using the Pythagorean theorem. We have the velocity of the plane heading west (200 mph) and the wind's velocity blowing S30°W (25 mph). To find the ground speed, we can treat these velocities as the components of a right triangle. Using the formula a^2 + b^2 = c^2, where a and b are the components and c is the hypotenuse, we have:
(200 mph)^2 + (25 mph)^2 = c^2
40,000 mph^2 + 625 mph^2 = c^2
40,625 mph^2 = c^2
c ≈ 201.57 mph
Therefore, the ground speed of the plane is approximately 201.57 mph.
2. When solving the triangle, the smallest angle is the angle opposite the shortest side. In this case, since 25 mph is the smallest side, the smallest angle is opposite to it.
3. The largest angle of the triangle is the angle opposite the longest side. In this case, since 201.57 mph is the longest side, the largest angle is opposite to it.
4. The remaining angle can be calculated by subtracting the sum of the two known angles from 180 degrees. Since we now know the smallest angle and the largest angle, we can calculate the remaining angle.
5. The bearing of the plane can be calculated using trigonometry. We have the wind's direction, S30°W, which is 30 degrees off the south direction. This means that the angle between the heading of the plane and due south is 30 degrees. By subtracting this angle from 180 degrees (since due south is 180 degrees from any direction), we can find the bearing of the plane.
*Please note that it is essential to double-check the calculations and consult your teacher or another reliable source for accurate answers.
Sure, I can help you with your questions!
1. To find the ground speed of the plane, we need to consider the effect of the wind. The ground speed of the plane is the vector sum of its airspeed (200 mph) and the velocity of the wind. To calculate the ground speed, we can use vector addition.
a. The component of the wind blowing in the west direction is 25 mph.
b. The component of the wind blowing in the south direction is 25 mph * sin(30°) ≈ 12.5 mph.
Now, we can find the ground speed by using the Pythagorean theorem:
Ground speed = √(airspeed^2 + (wind west)^2 + (wind south)^2)
= √(200^2 + 25^2 + 12.5^2)
= √(40,000 + 625 + 156.25)
≈ √40,781.25
≈ 202.4 mph (rounded to one decimal place)
Therefore, the ground speed of the plane is approximately 202.4 mph.
2. To solve the triangle, we need to use the Law of Cosines. Let's label the sides of the triangle as follows:
- The side opposite the smallest angle as side a
- The side opposite the angle formed by the plane's direction as side b
- The side opposite the angle formed by the wind's direction as side c
Now, we can use the formula for the Law of Cosines:
cos(A) = (b^2 + c^2 - a^2) / (2 * b * c)
By plugging in the values we know, we can find the smallest angle of the triangle.
3. To find the largest angle of the triangle, we can simply subtract the smallest angle from 180°. This is because the sum of all angles in a triangle is always 180°.
4. The remaining angle can be found by subtracting the largest angle from 180°. Since a triangle has three angles, this would be the third angle.
5. The bearing of the plane refers to the angle between the plane's direction and the north direction. It can be found using trigonometry. Let's define the angle between the north direction and the direction of the plane as angle A.
We can find the angle A by using the following formula:
tan(A) = (wind south) / (wind west)
By plugging in the given values, you can find the angle A. The bearing of the plane would then be 180° + A, since the plane is heading west.
I'm sorry to hear that you've been struggling with this problem for two months. Let's go through each question step by step to help you find the answers.
1. To find the ground speed of the plane, we need to consider the effect of both the plane's speed and the wind's speed. Since the plane is heading west at 200 mph and the wind is blowing in a different direction, we can use vector addition to determine the ground speed.
To do this, we need to break down the wind speed into its westward (W) and southward (S) components. For a 30 degree angle, we can use trigonometry to find the components:
W component = 25 mph * cos(30°)
S component = 25 mph * sin(30°)
Now, we can add the westward component of the plane's speed to the westward component of the wind's speed and the same for the southward component.
Ground speed = sqrt[(200 mph + W component)^2 + (S component)^2]
Calculating these values will give you the ground speed of the plane.
2. To find the smallest angle of the triangle, we need to consider the direction of the wind relative to the plane's path. In this case, the wind is blowing S30°W, which means it is 30 degrees westward from the south direction (180 degrees).
Since the plane is heading west, we can subtract the wind direction from the plane's direction to get the smallest angle:
Smallest angle = 180° - 30°
3. To find the largest angle of the triangle, we can consider that the sum of all angles in a triangle is 180 degrees. Since we have already found the smallest angle, we subtract that from 180 degrees to get the largest angle.
Largest angle = 180° - Smallest angle
4. To find the remaining angle, we can use the fact that the sum of all angles in a triangle is 180 degrees. So, we subtract the sum of the smallest and largest angles from 180 degrees.
Remaining angle = 180° - (Smallest angle + Largest angle)
5. To find the bearing of the plane, we need to consider the direction in which the plane is traveling relative to north. Since the plane is heading west, the bearing can be calculated as the angle between the plane's direction and the north direction.
Bearing = 180° - (180° - Smallest angle)
By following these steps, you should be able to find the answers to each of the questions. Remember to use the trigonometric functions (cos and sin) to calculate the wind's components and apply the rules of geometry to solve for the angles in the triangle.