What is the exact angle between the clock hands at 6:45:00 PM? Plz show work
2 answers:
Answer:
67.5°
Step-by-step explanation:
You know the long hand would be at number 9 and you also know that from the number 6 to 9 it would be 90°. Between each number, there are also 5 smaller marks on the clock. Thus, for 90°, there would be 5×3=15 smaller marks. (I used 3 because between 6 and 9 there are 3 big numbers)
Now here's the trickier part: There are 60 minutes within 5 small marks. We can find out at which mark does the shorter hand move to at 45 minutes.
×5 = 3.75
Out of the 15 smaller marks of 90°, the 45th minute stands at 3.75. The angle of 3.75 would then be between the 15th mark and the 3.75th mark. The gap would be 15-3.75 = 11.25 marks.
×90° = 67.5°
You can refer to the picture for better visualisation of the clock. Hope this helps.
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first off, often times some graphs say "not to scale", but sometimes that's accidental, sometimes is simply misleading, in this case is misleading.
since ∡ABC = ∡ACE, then the triangles look more or less like the ones in the picture on the right-hand-side.
and notice the red and green angle tickmarks, that simply means the triangles are similar by AA.
that said, we can use proportions, in this case from the large triangle's sides are atop and the small one's are at the bottom.