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Question 177536: 4. A triangle has two unknown angles A and B. If A is three times the size of B, and C = 39° 40’ 32” , find the magnitudes of A and B.
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! C = 39 degrees 40 minutes 32 seconds
32 seconds = 32/60 minutes = 32/60/60 degrees
40 minutes = 40/60 degrees
add those two together to get:
39.675555555..... degrees.
sum of angles of a triangle is 180.
180 - C = A + B = 180 - 39.6755555.... = 140.3244444...... degrees
A is 3 * B, so A + B is the same as B + 3*B = 4*B = 140.3244444..... degrees
this means that B = 140.324444...../4 = 35.0811111..... degrees
this means that A = 3*B = 105.2433333..... degrees
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if we round to the nearest thousandth of a degree, we get:
C = 39.676 degrees
A = 105.243 degrees
B = 35.081 degrees
sum of 39.676 + 105.243 + 35.081 = 180 degrees.
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A is 3 * B means that 3* 35.081 = 105.243 means that 105.243 = 105.243 means that this statement (A = 3*B) is true.
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the magnitudes are in decimals.
to convert back to degrees, minutes, and seconds, you need to convert the decimal portion to minutes and seconds.
do this as follows:
take the fractional part and multiply by 3600.
this gets you seconds.
divide those seconds by 60 to get minutes.
that would be the integer part of the division.
take the fractional part of the minutes and multiply by 60 to get the remaining seconds.
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to do this, use the unrounded answer, not the rounded answer, since the rounding will introduce some error in the result.
example:
C = 39.676 degrees
.676 * 3600 = 2433.6 seconds
2433.6 / 60 = 40.56 minutes
number of minutes is 40
number of seconds is .56 * 60 = 33.6 = 34 seconds
we know that the number of seconds is 32 because that was given.
the rounding introduced the error.
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go back and do it again with the unrounded value this time.
C = 39.675555555.... degrees
use .675555555.... * 3600 to get seconds (maximum digits the calculator has should do).
you get 2431.99999999.... seconds
divide that by 60 to get:
40.5333333...... minutes
multiply .5333333..... * 60 to get:
31.999999998 seconds
your answer is:
C = 39 degrees 40 minutes 32 seconds which agrees with the original value provided.
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do the same for A and B.
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A = 105.2433333..... degrees
.2433333.... * 3600 = 875.99999999.... seconds
.875.9999999.... / 60 = 14.6 minutes
.6 * 60 = 36 seconds
A = 105 degrees 14 minutes 36 seconds
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B = 35.0811111..... degrees
.0811111.... * 3600 = 292 seconds
292 / 60 = 4.866666666.... minutes
.866666666... * 60 = 52 seconds
B = 35 degrees 4 minutes 52 seconds
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you have:
A = 105 degrees 14 minutes 36 seconds
B = 35 degrees 4 minutes 52 seconds
C = 39 degrees 40 minutes 32 seconds
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add these together to get:
179 degrees 58 minutes 120 seconds
this adds up to 180 degrees so the conversion from decimals to minutes and seconds is good.
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your answer is:
A = 105 degrees 14 minutes 36 seconds
B = 35 degrees 4 minutes 52 seconds
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