An airplane is flying 20,500 feet above the ocean,forming a 20 angle of depression.A passenger looks out of his window and sees an island.Find the distance of the passenger's line of sight to the nearest thousandth. Needs to be drawn out and solved
Very strangely worded question, with two obvious mistakes / meaningless terms ("forming a 20 angle of depression" / "to the nearest thousandth"?).
But this is a trigonometry question, not inverse:
- Draw a straight horizontal line (the ground)
- Mark the plane somewhere above it. Draw a straight vertical line between the ground and the plane.
- Mark the island on the ground, somewhere ahead of the plane. Now join the plane and island with a diagonal line. This is the length you need to solve.
- You have a right-angled triangle now, with an angle at the island vertex of 20 degrees (assuming the question means that the line of sight from the plane to the island forms a 20 degree angle of depression; the way they have written it is meaningless nonsense).
So, you can solve the length using the property sin(theta) = o/h. Theta is 20 degrees, opposite side to the angle is the height of the plane, and the hypotentuse is what you're calculating.
You should get h = 20,500 / sin(20 deg)
(I wonder if they mean round to the nearest "thousand feet"... in which case it's 58,000 feet).
Mar 20th, 2015
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