Amanda and jamie are standing 25 feet apart and spot a bird in the sky between them the angle of elevation from Amanda is 25 fee
t apart and spot a bird in the sky between them the angle of elevation from Amanda to the bird is 55 and from Jamie to the bird is 63 how far away is the bird from Amanda
1 answer:
Answer:
25.2294 feet
Step-by-step explanation:
We can solve this question drawing a triangle using the values given and then using the law of sines. (See image attached to know how to draw the triangle and use the values).
First we need to find the third angle of the triangle, that is, the angle in the vertix where the bird is:
y + 55 + 63 = 180
y = 62°
The relation between the angles and the distances are:
25 / sin(y) = x / sin(63)
25 / 0.8829 = x / 0.8910
x = 25 * 0.8910 / 0.8829 = 25.2294 feet
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Using a z-table (http://www.z-table.com) we see that the area under the curve left of the score 350 would be 0.228. The area under the curve left of the score 400 would be 0.918. To find just the range between 350 and 400, we subtract the area left of 350 from the area left of 400; this will give us just from 350 to 400:
0.918-0.228 = 0.69.
We find the z-scores that correspond with each end of the range we're looking for. To find a z-score, we use the formula:
Using a z-table (http://www.z-table.com) we see that the area under the curve left of the score 350 would be 0.228. The area under the curve left of the score 400 would be 0.918. To find just the range between 350 and 400, we subtract the area left of 350 from the area left of 400; this will give us just from 350 to 400:
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Given:
In triangle ABC, .
To find:
The angle of depression from point A to point C.
Solution:
According to angle sum property, the sum of all interior angles of a triangle is 180 degrees.
In triangle ABC,
We know that if a transversal line intersect the two parallel lines, then alternate interior angles are equal. So, the angle of depression from point A to point C is equal to the measure of angle C in triangle ABC.
Therefore, the angle of depression is 24 degrees.