# Trigonometry tips: Angle of depression definiton

We will define angle of depression and understand the ways to find it along with the formula and examples. The angle made by an observer with the x-axis while looking at some object below the x-axis is called angle of depression. The figure below depicts this picture and explains the methodology as per angle of depression definition. As shown, an observer is looking at the downwards object while making an angle θ with the horizontal axis. Here θ can be called the angles of depression for an observer.

## Study of angle of depression formula:

The angle of depression formula will provide an easy yet effective way for solving angle of depression problems. As it is clear from the picture, the vertical drawn upwards from the object makes an right angle with the horizontal. In that case, knowing the depth of the target object and the horizontal distance is enough to find the angle θ. A trig formula is required in this case. We know that tangent of an angle is equal to the ratio of the opposite side to adjacent. Applying this concept, tanθ = Height / distance. The same formula holds true for finding the angle of elevation also.

## Let us solve angle of depression problems:

The angle of depression problem shown below removes all the curtains and makes the topic clear. It is highly important to study angle of depression word problem because its not just maths. It can be applied in many practical aspects in manufacturing civil structures.

(1) Find the horizontal distance of a ship sailing in the water while a man is looking it from the bridge at an angle of 40°. Assume height of the bridge as 280 m.

Height of the man can be neglected in comparison to that of the bridge. Now lets apply the tangent formula, tan 40 = Height / distance => D = 280 / tan 40 = 280 / 0.839 = 333.7 m.
Thus we have seen angle of depression word problems and had a detailed overview of the topic.

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