BIG IDEAS MATH
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The smaller acute angle measures
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Find the measure of each acute angle in a right triangle where
the measure of one acute angle is 3 times the sum of the measure of the
other acute angle and 8.
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Ck
B
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and the larger acute angle measures
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C
N
Let's represent the measure of one acute angle as x and the measure of the other acute angle as y. According to the problem, one acute angle is 3 times the sum of the other acute angle and 8. So we can write the equation:
x = 3(y + 8)
Since the sum of the measures of all angles in a triangle is 180 degrees, we can also write the equation:
x + y + 90 = 180
Now we can solve these equations to find the values of x and y.
From the first equation:
x = 3(y + 8)
x = 3y + 24
Now we substitute this value of x into the second equation:
(3y + 24) + y + 90 = 180
4y + 114 = 180
Now we solve for y:
4y = 180 - 114
4y = 66
y = 66/4
y = 16.5
Now we substitute this value of y back into the first equation to find x:
x = 3(16.5 + 8)
x = 3(24.5)
x = 73.5
So the measure of one acute angle is 73.5 degrees, and the measure of the other acute angle is 16.5 degrees.