- a = √(23² + 26²) = √(529 + 676) = √1205 ≈ 34.71 cm
- b = √(40² - 25²) = √(1600 - 625) = √975 ≈ 31.22 cm
- c = 52 × sin(41°) ≈ 52 × 0.6561 ≈ 34.12 cm
- d = 44 / cos(29°) ≈ 44 / 0.8746 ≈ 50.31 cm
- f = 27 × tan(56°) ≈ 27 × 1.4826 ≈ 40.03 cm
- g = arccos(27/32) ≈ arccos(0.8438) ≈ 32.47°
- h = arctan(6/18) = arctan(1/3) ≈ 18.43°
- i = 48 × sin(44°) ≈ 48 × 0.6947 ≈ 33.35 cm
- k = 35 / (2 × sin(18°)) ≈ 35 / (2 × 0.3090) ≈ 35 / 0.6180 ≈ 56.64 cm
- l = 26 × cos(41°) ≈ 26 × 0.7547 ≈ 19.62 cm
- m = 47 × sin(71°) ≈ 47 × 0.9455 ≈ 44.44 cm
- The side opposite the 78° angle is 7, and the side adjacent to it is 11. The included angle between sides of length 7 and 11 is not given directly, but since both are marked with single ticks, they are equal. This contradicts the given lengths. Assuming the diagram intends for the two marked sides to be equal, the problem is inconsistent. If we ignore the tick marks and use the given lengths, the third side can be found using the Law of Cosines: c² = 7² + 11² - 2×7×11×cos(78°) ≈ 49 + 121 - 154×0.2079 ≈ 170 - 32.02 ≈ 137.98, so c ≈ √137.98 ≈ 11.75 cm. However, given the ambiguity, this value may not be intended.
Parent Tip: Review the logic above to help your child master the concept of trigonometry basics worksheet.
