Respuesta :
Answer:
The length of the third side of fence is 11.4 m
Step-by-step explanation:
Solution:-
- We are to mow a triangular piece of land. We are given the description of motion and the orientation of land-mower while fencing.
- From one corner of the triangular land, the land-mower travels H1 = 5.7 m at θ1 = 0.3 radians north of east. We will use trigonometric ratios to determine the amount traveled ( B1 ) in the east direction.
[tex]cos ( theta_1 ) = \frac{B_1}{H_1}[/tex]
Where,
B1: Is the base length of the right angle triangle
H1: Hypotenuse of the right angle triangle
Therefore,
[tex]B_1 = H_1*cos ( theta_1 )\\\\B_1 = 5.7*cos ( 0.3 )\\\\B_1 = 5.44541 m[/tex]
- Similarly, from the other corner of the triangular land. The land-mower moves a lateral distance of H2 = 9m and directed θ2 = 0.9 radians north of west. We will use trigonometric ratios to determine the amount traveled ( B2 ) in the west direction.
[tex]cos ( theta_2 ) = \frac{B_2}{H_2} \\[/tex]
Where,
B2: Is the base length of the right angle triangle
H2: Hypotenuse of the right angle triangle
Therefore,
[tex]B_2 = H_2*cos ( theta_2 )\\\\B_2 = 9*cos(0.9)\\\\B_2 = 5.59448 m[/tex]
- The total length of the third side of the fence would be the sum of bases of the two right angles formed by the land-mower motion at each corner.
[tex]L = B_1 + B_2\\\\L = 5.44541 + 5.59448\\\\L = 11.4 m[/tex]
