# Angles of elevation and depression

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Suppose that you are looking at an object in the distance.

If the object is above you, then the angle of elevation is the angle your eyes look up.

If the object is below you, the angle of depression is the angle your eyes look down.

Angles of elevation and depression are measured from the horizontal.

It is common mistake not to measure the angle of depression from the horizontal.

Using the angle of depression or elevation to an object, and knowing how far away the object is, enables us to find the height of the object using trigonometry.

The advantage of doing this is that it is very difficult to measure the height of a mountain or the depth of a canyon directly; it is much easier to measure how far away it is (horizontal distance) and to measure the angle of elevation or depression.

Suppose that we want to find the height of this tree.

We mark point A and measure how far it is from the base of the tree.

Then we measure the angle of elevation from A to the top of the tree.

Now,

we have measured x and , so we can calculate tan() and thus we can find h, which is the height of the tree.

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### Question 1/5

1. A tree with angle of elevation 27o is 9m tall. How far away is the tree (to 1 decimal place)?

 16.5m 17.7m 15.4m 17.3m

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