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## What Is Angle of Elevation?

**Definition of elevation angle:** First we define the elevation angle. Let O and P be two points such that point P is at a higher level. Let OA and PB be horizontal lines through O and P respectively. If an observer is at O and the point P is the object under consideration, then the line OP is called the line of sight of the point P and the angle AOP, between the line of sight and the horizontal line OA, is known as to elevation angle of point P as seen from O. If an observer is at P and the object under consideration is at O, then the angle BPO is known as the angle of depression of O as seen from P .

**Elevation angle formula:** The formula we use for angle elevation is also known as angle of elevation. We can measure the angle of the sun relative to a right angle by the elevation of the angle. The horizon line drawn from the measurement angle to the sun at right angles is the elevation. Using opposite, hypotenuse and adjacent in a right triangle we can find the angle. elevation Of the right triangle the sin is opposite divided by the hypotenuse; cosine is adjacent divided by the hypotenuse; the tangent is opposite divided by adjacent. To understand the angle of elevation we will do a little

Elevation angle problems. Suppose the height of a tower is 100 sqrt(3) meters given. And we must find the elevation of the angle if its top from a point 100 meters away from its foot. So first we collect information, we know that the height of the given tower is 100 sqrt3 and the distance from the foot of the tower is 100m. Let’s take (theta) the angular elevation of the top of the tower…we’ll use the trigonometric relationship that contains base and perpendicular. This relationship is tangent. Using the tangent to the right triangle we have,

tan (theta) = perpendicular / adjacent

tan (theta) = 100 squared (3)/100 = squared (3).

tan (theta) = tan 60

theta = 60 degrees.

So the elevation angle will be 60 degrees

**Example: **The angle of elevation of the top of the tower from a point on the ground, which is 30 meters from the foot of the tower, is 30 degrees. Find the height of the tower.

**Solution: **Let AB be the top A of the tower h meters high and let C be a point on the ground such that the elevation of the angle from the top A of the tower AB is 30 degrees.

In the triangle ABC we have an angle C = 30 degrees and base BC = 30 and we have to find the perpendicular AB. Therefore, we use those trigonometric ratios that contain a base and a perpendicular. It is clear that this relationship is tangential. So we take the tangent of angle C.

In triangle ABC, taking the tangent of angle C, we have

so C = AB/AC

so 30 = AB/AC

1/sqrt(3) = h/30

h = 30/sqrt(3) meters = 10 sqrt(3) meters.

Therefore, the height of the tower is 10 square meters (3) meters.

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