Solve the triangle. B = 36°, a = 38, c = 18
1 answer:
Answer:
A ≈ 119.7°, b ≈ 25.7, C ≈ 24.3°
Step-by-step explanation:
A suitable app or calculator does this easily. (Since you're asking here, you're obviously not unwilling to use technology to help.)
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Given two sides and the included angle, the Law of Cosines can help you find the third side.
... b² = a² + c² - 2ac·cos(B)
... b² = 38² + 18² -2·38·18·cos(36°) ≈ 661.26475
... b ≈ 25.715
Then the Law of Sines can help you find the other angles. It can work well to find the smaller angle first (the one opposite the shortest side). That way, you can tell if the larger angle is obtuse or acute.
... sin(C)/c = sin(B)/b
... C = arcsin(c/b·sin(B)) ≈ 24.29515°
This angle and angle B add to less than 90°, so the remaining angle is obtuse. (∠A can also be found as 180° - ∠B - ∠C.)
... A = arcsin(a/b·sin(B)) ≈ 119.70485°
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The length of RS is 45 units if the perimeter of the rectangle below is 166 units.
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The question is incomplete.
The complete question is:
The perimeter of the rectangle below is 166 units. Find the length of the side RS. Write your answer without variables.
The figure is in the picture please refer to the picture.
The perimeter of the rectangle = 166 units
2(4x + 2 + 5x) = 166
9x + 2 = 83
9x = 81
x = 9
The length of RS = 5x = 5(9) = 45 units
Thus, the length of RS is 45 units if the perimeter of the rectangle below is 166 units
Learn more about the rectangle here:
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