+257 At 6 o'clock, the tip of the hour hand was 23cm from the tip of the minute hand. At 9 o'clock, this distance was only 17cm. By how many centimeters does the minute hand's length exceed the hour hand's length? ( no diagram provided) I tried to use Pythagorean and in the end, I didn't know what to do after I went from there.
At 6 o'clock, the tip of the hour hand was 23cm from the tip of the minute hand. At 9 o'clock, this distance was only 17cm. By how many centimeters does the minute hand's length exceed the hour hand's length? ( no diagram provided) I tried to use Pythagorean and in the end, I didn't know what to do after I went from there.
You were on the right track with Pythagorean. At six o'clock, the hands are in a straight line so we know the total length of the two hands is 23 cm. One hand length we will call L so the other hand is (23 – L).
Draw your triangle when the hour hand is at nine and the minute hand at twelve. One hand length is L, the other hand length is (23 – L), and the hypotenuse is 17.
so, by the Pythagorean Theorem, L2 + (23 – L)2 = 172
multiply it on out L2 + (529 – 46L + L2) = 289
remove parentheses and rearrange terms 2L2 – 46L + 240 = 0 (240 came from 529 minus 289)
this will factor to (2L – 16)(L – 15) = 0
set each term to zero 2L – 16 = 0 thus L = 8
L – 15 = 0 thus L = 15
the minute hand is longer, so it's the one that's 15 and the hour hand is 8
so the minute hand length exceeds the hour hand length by 15 – 8 = 7 cm
17 cm
At 6 o'clock, the tip of the hour hand was 23cm from the tip of the minute hand. At 9 o'clock, this distance was only 17cm. By how many centimeters does the minute hand's length exceed the hour hand's length? ( no diagram provided) I tried to use Pythagorean and in the end, I didn't know what to do after I went from there.
You were on the right track with Pythagorean. At six o'clock, the hands are in a straight line so we know the total length of the two hands is 23 cm. One hand length we will call L so the other hand is (23 – L).
Draw your triangle when the hour hand is at nine and the minute hand at twelve. One hand length is L, the other hand length is (23 – L), and the hypotenuse is 17.
so, by the Pythagorean Theorem, L2 + (23 – L)2 = 172
multiply it on out L2 + (529 – 46L + L2) = 289
remove parentheses and rearrange terms 2L2 – 46L + 240 = 0 (240 came from 529 minus 289)
this will factor to (2L – 16)(L – 15) = 0
set each term to zero 2L – 16 = 0 thus L = 8
L – 15 = 0 thus L = 15
the minute hand is longer, so it's the one that's 15 and the hour hand is 8
so the minute hand length exceeds the hour hand length by 15 – 8 = 7 cm
17 cm
