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Answer:
6. (A, B, C) ≈ (112.4°, 29.5°, 38.0°)
7. (a, b, C) ≈ (180.5, 238.5, 145°)
Step-by-step explanation:
My "work" is to make use of a triangle solver calculator. The results are attached. Triangle solvers are available for phone or tablet and on web sites. Many graphing calculators have triangle solvers built in.
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We suppose you're to make use of the Law of Sines and the Law of Cosines, as applicable.
6. When 3 sides are given, the Law of Cosines can be used to find the angles. For example, angle A can be found from ...
A = arccos((b² +c² -a²)/(2bc))
A = arccos((8² +10² -15²)/(2·8·10)) = arccos(-61/160) = 112.4°
The other angles can be found by permuting the variables appropriately.
B = arccos((225 +100 -64)/(2·15·10) = arccos(261/300) ≈ 29.5°
The third angle can be found as the supplement to the other two.
C = 180° -112.411° -29.541° = 38.048° ≈ 38.0°
The angles (A, B, C) are about (112.4°, 29.5°, 38.0°).
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7. When insufficient information is given for the Law of Cosines, the Law of Sines can be useful. It tells us side lengths are proportional to the sine of the opposite angle. With two angles, we can find the third, and with any side length, we can then find the other side lengths.
C = 180° -A -B = 145°
a = c(sin(A)/sin(C)) = 400·sin(15°)/sin(145°) ≈ 180.49
b = c(sin(B)/sin(C)) = 400·sin(20°)/sin(145°) ≈ 238.52
The measures (a, b, C) are about (180.5, 238.5, 145°).
Answer:
<em>The probability that the second ball is red is 71%</em>
Step-by-step explanation:
<u>Probabilities</u>
We know there are 5 red balls and 2 green balls. Let's analyze what can happen when two balls are drawn in sequence (no reposition).
The first ball can be red (R) or green (G). The probability that it's red is computed by
The probability is's green is computed by
If we have drawn a red ball, there are only 4 of them out of 6 in the urn, so the probability to draw a second red ball is
If we have drawn a green ball, there are still 5 red balls out of 6 in the urn, so the probability to draw a red ball now is
The total probability of the second ball being red is
The probability that the second ball is red is 71%