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Answer:
The bird is 2.44km high
Step-by-step explanation:
Hello,
To solve this question, we need to understand how they are and we can only get this with a correct pictorial diagram.
See attached document for better understanding.
From the first diagram, we understand that the bird is between them and also on top of them.
Assuming Susan, Mark and the bird all form a triangle at each other and the bird at the top, we can divide the the triangle into two equal parts.
But before then, we should know that sum of angles in a triangle is equal to 180°
Therefore,
20° + 50° + b° = 180
70° + b = 180
b = 180° - 70°
b = 110°
Dividing angle b into two equal parts = 55° on each side.
See the last attached document for better illustration.
Using SOHCAHTOA, we can find the adjacent of the triangle which corresponds to the height of the bird.
We have opposite = 3.4km and we're looking for adjacent. We can use tangent of the angle to find the adjacent.
Tanθ = opposite / adjacent
Tan 55° = 3.5 / adj
Adjacent = 3.5 / tan55
Adjacent = 3.5 / 1.43
Adjacent = 2.44km
The height of the bird is 2.44km
(-6,-4)
If you dilate a point, (c,d) about (a,b) by a scale factor by k. You'll going to subtract each coordinates where the point will be dilated about (a,b) from the point (c,d) and then multiply them by k. This would be the formula if you want: (k(c -a), k(b -d))
Let's say F is the dilation of D about the origin or (0,0) then the x coordinate of F would be
This would be the y coordinate of F:
Thus the coordinates of F is (-6,-4)