*• From the top of a fire tower, a forest ranger sees his partner on the ground at an angle of depression of 40º.*

Find to the is a support wire used to hold a newly planted tree in place, preventing it from bending or up-rooting during high winds. • It is assumed that the tree is vertical, making it perpendicular with the ground.

• This problem deals with "opposite" and "hypotenuse" making it a sine problem.

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Try it risk-free In this lesson, you'll explore the difference between angles of elevation and depression.

An eight foot wire is attached to the tree and to a stake in the ground.

From the stake in the ground the angle of elevation of the connection with the tree is 42º.This fits with the rule that the angle of elevation and the angle of depression must be the same.If someone were unwisely standing on the ground where the plane is about to land and looking up at the plane, the angle of elevation of their gaze would be the same as the angle of depression of the pilot's gaze; in this case, they're both 30 degrees.Will the plane make it to the runway before it hits the ground and if so, how many miles from the end of the runway will it touch down? The problem tells us that the angle of depression is 30 degrees.In other words, if the pilot looked straight forward out of the cockpit window, his gaze would be tilted down 30 degrees below an imaginary horizontal line parallel to the ground.• This solution deals with "opposite" and "adjacent" making it a tangent problem. From a point 87 feet from the base of the tower, the angle of elevation of the top of the first section is 25º, and the angle of elevation of the top of the second section is 40º.As a member, you'll also get unlimited access to over 79,000 lessons in math, English, science, history, and more.The answer: you can make mathematical models of all of them with angles of elevation and depression!If a person is standing on the ground, looking up at something in the sky, the angle of elevation is the angle formed between the person's line of sight and the ground.• It is assumed that the tower is vertical, making it perpendicular with the ground.• This solution will use alternate interior angles from the parallel horizontal lines, so place 40º inside the triangle by the partner (bottom right).

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