Day 3:
1. To find the missing side a, we can use the Pythagorean theorem: a^2 + b^2 = c^2
Substituting the given values, we get: a^2 + 17^2 = 23^2
Simplifying and solving for a, we get: a = sqrt(23^2 - 17^2) = 12 cm
Therefore, the missing side a is 12 cm.
2. To find the missing side b, we can again use the Pythagorean theorem: b^2 = c^2 - a^2
Substituting the given values, we get: b^2 = 23^2 - 12^2
Simplifying and solving for b, we get: b = sqrt(23^2 - 12^2) = 19 cm
Therefore, the missing side b is 19 cm.
Day 4:
1. To find the missing side b, we can use the trigonometric ratio tangent: tan(A) = b / a
Substituting the given values, we get: tan(15) = b / c
Simplifying and solving for b, we get: b = c * tan(15) / 1
Substituting the given value of c, we get: b = 37 * tan(15) / 1 = 9.5 cm
Therefore, the missing side b is 9.5 cm.
2. To find the missing side a, we can use the trigonometric ratio cosine: cos(B) = a / c
Substituting the given values, we get: cos(64) = a / 19.2
Simplifying and solving for a, we get: a = 19.2 * cos(64) / 1
Substituting the given value of c, we get: a = 7.15 cm
Therefore, the missing side a is 7.15 cm.
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Answers & Comments
Day 3:
1. To find the missing side a, we can use the Pythagorean theorem: a^2 + b^2 = c^2
Substituting the given values, we get: a^2 + 17^2 = 23^2
Simplifying and solving for a, we get: a = sqrt(23^2 - 17^2) = 12 cm
Therefore, the missing side a is 12 cm.
2. To find the missing side b, we can again use the Pythagorean theorem: b^2 = c^2 - a^2
Substituting the given values, we get: b^2 = 23^2 - 12^2
Simplifying and solving for b, we get: b = sqrt(23^2 - 12^2) = 19 cm
Therefore, the missing side b is 19 cm.
Day 4:
1. To find the missing side b, we can use the trigonometric ratio tangent: tan(A) = b / a
Substituting the given values, we get: tan(15) = b / c
Simplifying and solving for b, we get: b = c * tan(15) / 1
Substituting the given value of c, we get: b = 37 * tan(15) / 1 = 9.5 cm
Therefore, the missing side b is 9.5 cm.
2. To find the missing side a, we can use the trigonometric ratio cosine: cos(B) = a / c
Substituting the given values, we get: cos(64) = a / 19.2
Simplifying and solving for a, we get: a = 19.2 * cos(64) / 1
Substituting the given value of c, we get: a = 7.15 cm
Therefore, the missing side a is 7.15 cm.