A drone flies at 10 m/s, 25° above the horizontal. Enter the horizontal component of its velocity in m/s, to one decimal place.
A component diagram can look tidy and still be wrong. The drawing is easy to check with a ruler. The labels are where the errors hide.
A diagram resolves a 30 m/s velocity at 35° above the horizontal. Three labels sit on three sides. Which label belongs where?
Check the hypotenuse first. The slanted side is the vector itself, so it carries the full magnitude: 30 m/s. Check the leg next to the marked angle second. The adjacent side carries the cosine: 30 cos 35°.
Check the leg opposite the marked angle third. That side carries the sine: 30 sin 35°. Check the corner where the legs meet last. The two components are perpendicular, so the legs meet at 90°.
A diagram resolves a 32 m/s velocity at 25° above the horizontal. The leg adjacent to the 25° angle is labelled 32 cos 25°, the opposite leg 32 sin 25°, and the hypotenuse 32 m/s. Is the diagram correct?
Here is the same diagram with one label changed: the adjacent leg now reads 30 sin 35°. Sine belongs on the opposite side. The diagram has swapped sine and cosine. It is wrong.
A diagram resolves a 26 m/s velocity at 40° above the horizontal. The leg adjacent to the 40° angle is labelled 26 sin 40°, and the opposite leg is labelled 26 cos 40°. Is the diagram correct?
Here is the diagram again with a different change: the horizontal leg now reads 30 m/s, and the hypotenuse reads 30 cos 35°. The full magnitude belongs on the hypotenuse, not on a leg. It is wrong.
Here it is once more. The labels are right, but the horizontal leg overshoots and the second leg leans back, so the legs meet at 60°. Components are perpendicular. It is wrong.
A diagram shows a 16 m/s velocity at 42° above the horizontal. The hypotenuse is labeled 16 m/s, the leg adjacent to the 42° angle is labeled 16 cos 42°, the opposite leg is labeled 16 sin 42°, and the legs meet at 90°. Judge the diagram.
Check the hypotenuse: it carries the full magnitude, 16 m/s. Pass.
Check the adjacent leg: it carries the cosine, 16 cos 42°. Pass.
Check the opposite leg: it carries the sine, 16 sin 42°. Pass.
Check the corner: the legs meet at 90°. Pass.
The diagram passes all four checks. It is correct.
A diagram resolves a 45 m/s velocity at 55° above the horizontal. The leg opposite the 55° angle is labelled 45 cos 55°, and the adjacent leg is labelled 45 sin 55°. Which error does the diagram make?
A diagram shows a 38 m/s velocity at 50° above the horizontal. The leg parallel to the ground is labelled 38 m/s, and the hypotenuse is labelled 38 cos 50°. The diagram is wrong. Which error does it make?
A diagram resolves a 54 m/s velocity at 35° above the horizontal. Which labelling is correct?
A diagram shows a 20 m/s velocity at 30° above the horizontal. The leg labelled 20 cos 30° lies parallel to the ground; the leg labelled 20 sin 30° leans so the two legs meet at 60°. The diagram is wrong. Which error does it make?