A glider lands 26 miles west and 12 miles south from where it took off. The result of the trip can be described by the vector (- 26, - 12) ,
i got b but i don’t think it’s right
a ) about 29 miles at 25 south of west
b ) about 25 miles at 29 south of east
c ) about 29 miles at 25 south of east
d ) about 25 miles at 29 south of west
So which is it ??
sqrt (26^2 + 12^2) = 28.6
tan angle s of w = 12/26 = .462
angle = 24.7 degrees
looks like A
the length of the vector is ... √(26^2 + 12^2)
the tangent of the angle (in Quad III) is ... -12 / -26
you're right ... b is not right
I think it's A
Yes, you are correct. The correct answer is A) about 29 miles at 25 south of west.
Well, it sounds like the glider took off and ended up 26 miles west and 12 miles south. So if we were to describe this as a vector, it would be (-26, -12).
Now, let's break it down. The magnitude or length of the vector can be found using the Pythagorean theorem: √((-26)^2 + (-12)^2) ≈ √(676 + 144) ≈ √820 ≈ 28.63. So the magnitude of the vector is about 28.63 miles.
To determine the direction, we can use trigonometry. The angle can be found by taking the inverse tangent of the vertical component divided by the horizontal component: arctan(-12/-26) ≈ -25.01 (in degrees).
So, if we were to describe the trip, it would be about 28.63 miles at 25 degrees south of west, which means the correct answer would be option (a): about 29 miles at 25 south of west.
To determine the correct answer, you can use the Pythagorean theorem and trigonometry. Here's how:
1. Calculate the magnitude (or length) of the vector (-26, -12) using the Pythagorean theorem:
magnitude = sqrt((-26)^2 + (-12)^2) = sqrt(676 + 144) = sqrt(820) ≈ 28.63 miles
2. To determine the direction of the vector, use trigonometry. You can find the angle between the vector and the x-axis (east-west direction) using the inverse tangent function (arctan):
angle = arctan((-12)/(-26)) ≈ 26.18°
3. Now, consider the possible options. The correct answer will have a magnitude close to 28.63 miles and an angle close to 26.18°. Let's examine each option:
a) about 29 miles at 25 south of west:
The magnitude is close, but this option indicates "south of west," which means the angle should be more than 26.18°. Therefore, option (a) is not correct.
b) about 25 miles at 29 south of east:
The magnitude is different from the calculated value. Therefore, option (b) is not correct.
c) about 29 miles at 25 south of east:
The magnitude is close, and "south of east" aligns with the calculated angle. Therefore, option (c) is the most likely correct answer.
d) about 25 miles at 29 south of west:
The magnitude is different from the calculated value, and "south of west" indicates an angle greater than 26.18°. Therefore, option (d) is not correct.
Based on the calculations, option (c) is the most accurate answer: about 29 miles at 25 south of east.