Quadrilateral - irregular

Find the length of the side d = |AD| in quadrilateral ABCD: a= 35m, b= 120m, c=85m, angle ABC = 105 degrees, angle BCD= 72 degrees

Correct answer:

d = 113.0411 m

Step-by-step explanation:

a = 35 m b = 120 m c = 85 m β = 105^{\circ} γ = 72^{\circ} B_{2} = 180 - β = 180 - 105 = 75^{\circ} C_{2} = B_{2} + (180 - γ) = 75 + (180 - 72) = 183^{\circ} A = (0, 0) B = (a, 0) C = (C_{x}, C_{y}) D = (D_{x}, D_{y}) C_{x} = B_{x} + b \cdot cos B_{2} = B_{x} + b \cdot cos 75 ° = 35 + 120 \cdot cos 75 ° = 35 + 120 \cdot 0.258819 = 66.05829 C_{y} = B_{y} + b \cdot sin B_{2} = B_{y} + b \cdot sin 75 ° = 0 + 120 \cdot sin 75 ° = 0 + 120 \cdot 0.965926 = 115.9111 D_{x} = C_{x} + c \cdot cos C_{2} = C_{x} + c \cdot cos 183 ° = 66.0583 + 85 \cdot cos 183 ° = 66.0583 + 85 \cdot (- 0.99863) = - 18.82523 D_{y} = C_{y} + c \cdot sin C_{2} = C_{y} + c \cdot sin 183 ° = 115.9111 + 85 \cdot sin 183 ° = 115.9111 + 85 \cdot (- 0.052336) = 111.46254 d = d i s t (A, D) = ∣ A D ∣ = (A_{x} - D_{x})^{2} + (A_{y} - D_{y})^{2} = (0 - (- 18.8252))^{2} + (0 - 111.4625)^{2} = 113.0411 m

Did you find an error or inaccuracy? Feel free to write us. Thank you!

Tips for related online calculators

Do you want to convert length units?
See also our right triangle calculator.
See also our trigonometric triangle calculator.
Try conversion angle units angle degrees, minutes, seconds, radians, grads.

You need to know the following knowledge to solve this word math problem:

Units of physical quantities:

Grade of the word problem:

We encourage you to watch this tutorial video on this math problem: video1 video2 video3

Related math problems and questions: