Trigonometry: 1) Work out the bearing from B to C. 2) Calculate the bearing of D from B
1 answer:
Answer:
see below
Step-by-step explanation:
a bearing is the angle in degrees measured clockwise from north.
Triangle ABC is a right triangle
Tan C = opp side / hyp
tan C = AB / CA
tan C = 30/30
tan C = 1
taking the inverse tan
tan ^ -1 tan C = tan ^ -1 ( 1)
C = 45 degrees
This is 90+45 degrees from North
135 degrees from north
Tan B = opp side / hyp
tan B = AD/BA
tan B = 45/30
tan B = 3/2
taking the inverse tan
tan ^ -1 tan B = tan ^ -1 ( 3/2)
D = 56.30993247
Add 180 degrees
180+56.30993247
236.3099325 from north
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Explanation:
When the inequality symbol is replaced by an equal sign, the resulting linear equation is the boundary of the solution space of the inequality. Whether that boundary is included in the solution region or not depends on the inequality symbol.
The boundary line is included if the symbol includes the "or equal to" condition (≤ or ≥). An included boundary line is graphed as a solid line.
When the inequality symbol does not include the "or equal to" condition (< or >), the boundary line is not included in the solution space, and it is graphed as a dashed line.
Once the boundary line is graphed, the half-plane that makes up the solution space is shaded. The shaded half-plane will be to the right or above the boundary line if the inequality can be structured to be of one of these forms:
- x > ... or x ≥ ... ⇒ shading is to the right of the boundary
- y > ... or y ≥ ... ⇒ shading is above the boundary
Otherwise, the shaded solution space will be below or to the left of the boundary line.
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Just as a system of linear equations may have no solution, so that may be the case for inequalities. If the boundary lines are parallel and the solution spaces do not overlap, then there is no solution.
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The attached graph shows an example of graphed inequalities. The solutions for this system are in the doubly-shaded area to the left of the point where the lines intersect. We have purposely shown both kinds of inequalities (one "or equal to" and one not) with shading both above and below the boundary lines.
